Edit Profile Gogatishvili, Amiran Compute Distance To: Compute Author ID: gogatishvili.amiran Published as: Gogatishvili, A.; Gogatishvili, A. S.; Gogatishvili, Amiram; Gogatishvili, Amiran Homepage: http://users.math.cas.cz/~gogatish/ External Links: Math-Net.Ru Documents Indexed: 117 Publications since 1988, including 2 Books Reviewing Activity: 31 Reviews all top 5 Co-Authors 14 single-authored 20 Opic, Bohumír 18 Mustafayev, Rza Ch. 15 Pick, Luboš 13 Kokilashvili, Vakhtang Mikhailovich 10 Neves, Júlio Severino 10 Persson, Lars-Erik 8 Kopaliani, Tengiz 6 Stepanov, Vladimir Dmitrievich 5 Fiorenza, Alberto 5 Genebashvili, Ioseb 5 Kufner, Alois 4 Caetano, António M. 4 Ünver, Tuğçe 3 Evans, William Desmond 3 Formica, Maria Rosaria 3 Guliyev, Vagif Sabir 3 Koskela, Pekka 3 Krbec, Miroslav 3 Soudský, Filip 2 Agcayazi, Mujdat 2 Burenkov, Viktor Ivanovich 2 Carro, María Jesús 2 Dai, Feng 2 Edmunds, David Eric 2 Křepela, Martin 2 Martín, Joaquim 2 Ovchinnikov, Vladimir I. 2 Rakotoson, Jean-Michel 2 Sobukawa, Takuya 2 Trebels, Walter 2 Wall, Peter 2 Wedestig, Anna 2 Yang, Dachun 2 Yuan, Wen 1 Ahmed, Irshaad 1 Aykol, Canay 1 Bernardis, Ana L. 1 Cobos, Fernando 1 Danelia, Anna 1 Genebashvili, I. Z. 1 Goginava, Ushangi 1 Johansson, Maria 1 Kerman, Ron 1 Koca, Kerim 1 Kuliev, Komil D. 1 Kulieva, Gulchehra 1 Lang, Jan 1 Martín-Reyes, Francisco Javier 1 Moritoh, Shinya 1 Domingues de Moura, Susana 1 Niwa, Miyuki 1 Okpoti, Christopher Adjei 1 Ol’hava, Rastislav 1 Ortega Salvador, Pedro 1 Samashvili, Nino 1 Schneider, Jan 1 Shanmugalingam, Nageswari 1 Tephnadze, George 1 Tikhonov, Sergey Yur’evich 1 Zhou, Yuan all top 5 Serials 6 Mathematische Nachrichten 6 Georgian Mathematical Journal 6 Mathematical Inequalities & Applications 5 Czechoslovak Mathematical Journal 4 Journal of Mathematical Analysis and Applications 4 Journal of Functional Analysis 4 Doklady Mathematics 3 Studia Mathematica 3 Journal of Approximation Theory 3 Real Analysis Exchange 3 Soobshcheniya Akademii Nauk Gruzinskoĭ SSR 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Eurasian Mathematical Journal 2 Collectanea Mathematica 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Publicacions Matemàtiques 2 Soobshcheniya Akademii Nauk Gruzii 2 Potential Analysis 2 The Journal of Fourier Analysis and Applications 2 Journal of Inequalities and Applications 2 Proceedings of A. Razmadze Mathematical Institute 2 Mediterranean Journal of Mathematics 1 Bulletin of the Australian Mathematical Society 1 Russian Mathematical Surveys 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Archiv der Mathematik 1 Canadian Mathematical Bulletin 1 Indiana University Mathematics Journal 1 Journal of Computational and Applied Mathematics 1 Journal of the London Mathematical Society. Second Series 1 Journal of the Mathematical Society of Japan 1 Mathematica Slovaca 1 Mathematische Zeitschrift 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Soviet Mathematics. Doklady 1 Tokyo Journal of Mathematics 1 Soochow Journal of Mathematics 1 Journal of Operator Theory 1 Zeitschrift für Analysis und ihre Anwendungen 1 Acta Mathematica Hungarica 1 Forum Mathematicum 1 Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences 1 Proceedings of the Georgian Academy of Sciences. Mathematics 1 Bulletin des Sciences Mathématiques 1 Nonlinear Studies 1 Positivity 1 Revista Matemática Complutense 1 Bulletin of TICMI 1 Vestnik Voronezhskogo Gosudarstvennogo Universiteta. Seriya Fizika, Matematika 1 Journal of Function Spaces and Applications 1 Complex Variables and Elliptic Equations 1 Banach Journal of Mathematical Analysis 1 Proceedings of the Estonian Academy of Sciences 1 Differential Equations and Applications all top 5 Fields 81 Functional analysis (46-XX) 52 Real functions (26-XX) 50 Harmonic analysis on Euclidean spaces (42-XX) 19 Operator theory (47-XX) 4 Partial differential equations (35-XX) 4 Integral transforms, operational calculus (44-XX) 3 Abstract harmonic analysis (43-XX) 2 Measure and integration (28-XX) 1 Approximations and expansions (41-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 92 Publications have been cited 850 times in 468 Documents Cited by ▼ Year ▼ Boundedness of the fractional maximal operator in local Morrey-type spaces. Zbl 1207.42015Burenkov, V. I.; Gogatishvili, A.; Guliyev, V. S.; Mustafayev, R. Ch. 56 2010 Weight theory for integral transforms on spaces of homogeneous type. Zbl 0955.42001Genebashvili, I.; Gogatishvili, A.; Kokilashvili, V.; Krbec, M. 56 1998 Limiting reiteration for real interpolation with slowly varying functions. Zbl 1080.46012Gogatishvili, Amiran; Opic, Bohumír; Trebels, Walter 40 2005 Discretization and anti-discretization of rearrangement-invariant norms. Zbl 1066.46023Gogatishvili, Amiran; Pick, Luboš 37 2003 Reduction theorems for weighted integral inequalities on the cone of monotone functions. Zbl 1288.26018Gogatishvili, A.; Stepanov, V. D. 34 2013 Characterizations of Besov and Triebel-Lizorkin spaces on metric measure spaces. Zbl 1278.42029Gogatishvili, Amiran; Koskela, Pekka; Zhou, Yuan 32 2013 Boundedness of the Riesz potential in local Morrey-type spaces. Zbl 1223.42008Burenkov, Victor I.; Gogatishvili, Amiran; Guliyev, Vagif S.; Mustafayev, Rza Ch. 32 2011 Weighted inequalities for Hardy-type operators involving suprema. Zbl 1116.47041Gogatishvili, Amiran; Opic, Bohumír; Pick, Luboš 31 2006 Interpolation properties of Besov spaces defined on metric spaces. Zbl 1195.46033Gogatishvili, Amiran; Koskela, Pekka; Shanmugalingam, Nageswari 25 2010 The generalized Hardy operator with kernel and variable integral limits in Banach function spaces. Zbl 0947.47020Gogatishvili, A.; Lang, J. 24 1999 Weighted inequalities involving two Hardy operators with applications to embeddings of function spaces. Zbl 1150.26001Carro, María; Gogatishvili, Amiran; Martín, Joaquim; Pick, Luboš 19 2008 A reduction theorem for supremum operators. Zbl 1127.26012Gogatishvili, Amiran; Pick, Luboš 18 2007 An equivalence theorem for integral conditions related to Hardy’s inequality. Zbl 1070.26015Gogatishvili, Amiram; Kufner, Alois; Persson, Lars-Erik; Wedestig, Anna 18 2004 New pre-dual space of Morrey space. Zbl 1263.46031Gogatishvili, A.; Mustafayev, R. Ch. 17 2013 Sharp embeddings of Besov spaces involving only logarithmic smoothness. Zbl 1161.46017Caetano, António M.; Gogatishvili, Amiran; Opic, Bohumir 17 2008 Functional properties of rearrangement invariant spaces defined in terms of oscillations. Zbl 1110.46012Carro, María J.; Gogatishvili, Amiran; Martín, Joaquim; Pick, Luboš 17 2005 A note on maximal commutators and commutators of maximal functions. Zbl 1330.42012Agcayazi, Mujdat; Gogatishvili, Amiran; Koca, Kerim; Mustafayev, Rza 16 2015 Reduction theorems for operators on the cones of monotone functions. Zbl 1326.47063Gogatishvili, Amiran; Stepanov, Vladimir D. 16 2013 Embeddings and duality theorem for weak classical Lorentz spaces. Zbl 1106.26018Gogatishvili, Amiran; Pick, Luboš 16 2006 Weighted iterated Hardy-type inequalities. Zbl 1375.26032Gogatishvili, Amiran; Mustafayev, Rza Ch. 13 2017 Some new iterated Hardy-type inequalities. Zbl 1260.26023Gogatishvili, A.; Mustafayev, R. Ch.; Persson, L.-E. 13 2012 On grand and small Lebesgue and Sobolev spaces and some applications to PDE’s. Zbl 1398.46025Fiorenza, Alberto; Formica, Maria Rosaria; Gogatishvili, Amiran 10 2018 Characterizations of Besov and Triebel-Lizorkin spaces via averages on balls. Zbl 1331.46023Dai, Feng; Gogatishvili, Amiran; Yang, Dachun; Yuan, Wen 10 2016 Characterizations of Sobolev spaces via averages on balls. Zbl 1346.46023Dai, Feng; Gogatishvili, Amiran; Yang, Dachun; Yuan, Wen 10 2015 Ulyanov-type inequalities between Lorentz-Zygmund spaces. Zbl 1316.41010Gogatishvili, Amiran; Opic, Bohumír; Tikhonov, Sergey; Trebels, Walter 10 2014 Characterisation of embeddings in Lorentz spaces. Zbl 1128.26012Gogatishvili, A.; Johansson, M.; Okpoti, C. A.; Persson, L.-E. 10 2007 Embeddings and the growth envelope of Besov spaces involving only slowly varying smoothness. Zbl 1238.46024Caetano, António M.; Gogatishvili, Amiran; Opic, Bohumír 9 2011 Optimal embeddings of Bessel-potential-type spaces into generalized Hölder spaces involving \(k\)-modulus of smoothness. Zbl 1197.46017Gogatishvili, Amiran; Neves, Júlio S.; Opic, Bohumír 9 2010 Some new scales of weight characterizations of the class \(B_p\). Zbl 1199.26057Gogatishvili, A.; Kufner, A.; Persson, L.-E. 9 2009 Characterization of associate spaces of weighted Lorentz spaces with applications. Zbl 1325.46032Gogatishvili, Amiran; Pick, Luboš; Soudský, Filip 8 2014 Some new iterated Hardy-type inequalities: the case \({\theta=1}\). Zbl 1297.26035Gogatishvili, Amiran; Mustafayev, Rza; Persson, Lars-Erik 8 2013 Dual spaces of local Morrey-type spaces. Zbl 1249.46020Gogatishvili, Amiran; Mustafayev, Rza 8 2011 Optimality of embeddings of Bessel-potential-type spaces into Lorentz-Karamata spaces. Zbl 1076.46021Gogatishvili, Amiran; Opic, Bohumír; Neves, Júlio S. 8 2004 Duality principles and reduction theorems. Zbl 0985.46013Gogatishvili, Amiran; Pick, Luboš 8 2000 Characterization of interpolation between grand, small or classical Lebesgue spaces. Zbl 1409.46025Fiorenza, Alberto; Formica, Maria Rosaria; Gogatishvili, Amiran; Kopaliani, Tengiz; Rakotoson, Jean Michel 7 2018 Compact embeddings of Bessel-potential-type spaces into generalized Hölder spaces involving \(k\)-modulus of smoothness. Zbl 1213.46029Gogatishvili, Amiran; Neves, Júlio S.; Opic, Bohumír 7 2011 Sharp estimates of the \(k\)-modulus of smoothness of Bessel potentials. Zbl 1194.26026Gogatishvili, Amiran; Neves, Júlio S.; Opic, Bohumír 7 2010 Optimal embeddings and compact embeddings of Bessel-potential-type spaces. Zbl 1179.46029Gogatishvili, Amiran; Neves, Júlio S.; Opic, Bohumír 7 2009 Embeddings of Lorentz-type spaces involving weighted integral means. Zbl 1383.46023Gogatishvili, Amiran; Křepela, Martin; Pick, Luboš; Soudský, Filip 6 2017 Sharpness and non-compactness of embeddings of Bessel-potential-type spaces. Zbl 1137.46020Gogatishvili, Amiran; Neves, Júlio Severino; Opic, Bohumír 6 2007 Solution of two-weight problems for integral transforms with positive kernels. Zbl 1056.42507Genebashvili, I.; Gogatishvili, A.; Kokilashvili, V. 6 1996 Criteria of weighted inequalities in Orlicz classes for maximal functions defined on homogeneous type spaces. Zbl 0819.42007Gogatishvili, A.; Kokilashvili, V. 6 1994 Criteria of general weak type inequalities for integral transforms with positive kernels. Zbl 0803.42011Genebashvili, I.; Gogatishvili, A.; Kokilashvili, V. 6 1993 Iterated Hardy-type inequalities involving suprema. Zbl 1379.26018Gogatishvili, Amiran; Mustafayev, Rza Ch. 5 2017 The rearrangement-invariant space \(\Gamma _{p,\phi}\). Zbl 1311.46025Gogatishvili, Amiran; Kerman, Ron 5 2014 The reverse Hardy inequality with measures. Zbl 1136.26004Evans, W. Desmond; Gogatishvili, Amiran; Opic, Bohumír 5 2008 Optimality of embeddings of Bessel-potential-type spaces into generalized Hölder spaces. Zbl 1096.46016Gogatishvili, Amiran; Neves, Júlio S.; Opic, Bohumír 5 2005 Weak and extra-weak type inequalities for the maximal operator and the Hilbert transform. Zbl 0798.42009Gogatishvili, Amiran; Pick, Luboš 5 1993 Weak-type estimates in Morrey spaces for maximal commutator and commutator of maximal function. Zbl 1401.42018Gogatishvili, Amiran; Mustafayev, Rza; Aǧcayazi, Müjdat 4 2018 Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces. Zbl 1432.46013Caetano, António; Gogatishvili, Amiran; Opic, Bohumír 4 2016 Local Hardy-Littlewood maximal operator in variable Lebesgue spaces. Zbl 1285.42018Gogatishvili, A.; Danelia, A.; Kopaliani, T. 4 2014 Equivalence of norms of Riesz potential and fractional maximal function in generalized Morrey spaces. Zbl 1258.42017Gogatishvili, Amiran; Mustafayev, Rza 4 2012 Integral operators on cones of monotone functions. Zbl 1281.26014Gogatishvili, A.; Stepanov, V. D. 4 2012 Interpolation orbits and optimal Sobolev’s embeddings. Zbl 1137.46021Gogatishvili, Amiran; Ovchinnikov, Vladimir I. 4 2007 Criteria of strong type two-weighted inequalities for fractional maximal functions. Zbl 0884.42015Gogatishvili, A.; Kokilashvili, V. 4 1996 Maximal functions, \(\varphi(L)\) classes and Carleson measures. Zbl 0815.42010Gogatishvili, A.; Kokilashvili, V.; Krbec, M. 4 1993 A note on boundedness of the Hardy-Littlewood maximal operator on Morrey spaces. Zbl 1346.42017Gogatishvili, A.; Mustafayev, R. Ch. 3 2016 Characterization of associate spaces of generalized weighted weak-Lorentz spaces and embeddings. Zbl 1361.46022Gogatishvili, Amiran; Aykol, Canay; Guliyev, Vagif S. 3 2015 Embeddings of Sobolev-type spaces into generalized Hölder spaces involving \(k\)-modulus of smoothness. Zbl 1318.26045Gogatishvili, Amiran; Moura, Susana D.; Neves, Júlio S.; Opic, Bohumír 3 2015 Some scales of equivalent conditions to characterize the Stieltjes inequality: the case \(q<p\). Zbl 1298.26052Gogatishvili, Amiran; Persson, Lars-Erik; Stepanov, Vladimir D.; Wall, Peter 3 2014 Boundedness of Stein’s spherical maximal function in variable Lebesgue spaces and application to the wave equation. Zbl 1267.42019Fiorenza, Alberto; Gogatishvili, Amiran; Kopaliani, Tengiz 3 2013 The weighted Stieltjes inequality and applications. Zbl 1268.26026Gogatishvili, Amiran; Kufner, Alois; Persson, Lars-Erik 3 2013 Characterization of a rearrangement-invariant hull of a Besov space via interpolation. Zbl 1357.46030Gogatishvili, Amiran; Pick, Luboš; Schneider, Jan 3 2012 On scales of equivalent conditions characterizing weighted Stieltjes inequality. Zbl 1261.42005Gogatishvili, A.; Persson, L.-E.; Stepanov, V. D.; Wall, P. 3 2012 Integral operators on cones of monotone functions. Zbl 1263.47057Gogatishvili, A.; Stepanov, V. D. 3 2012 Compact embeddings of Besov spaces involving only slowly varying smoothness. Zbl 1249.46026Caetano, A.; Gogatishvili, A.; Opic, B. 3 2011 Solutions of some weight problems. Zbl 0806.46031Genebashvili, Ioseb; Gogatishvili, Amiran; Kokilashvili, Vakhtang 3 1993 General weak type inequalities for the maximal operators and singular integrals. Zbl 0790.42008Gogatishvili, A. 3 1992 Some new results related to Lorentz \(G\Gamma\)-spaces and interpolation. Zbl 1442.46014Ahmed, Irshaad; Fiorenza, Alberto; Formica, Maria Rosaria; Gogatishvili, Amiran; Rakotoson, Jean Michel 2 2020 Construction of function spaces close to \(L^\infty \) with associate space close to \(L^1\). Zbl 1425.46017Edmunds, David; Gogatishvili, Amiran; Kopaliani, Tengiz 2 2018 Embeddings between weighted Copson and Cesàro function spaces. Zbl 06819576Gogatishvili, Amiran; Mustafayev, Rza; Ünver, Tuğçe 2 2017 Interpolation of uniformly absolutely continuous operators. Zbl 1273.46011Cobos, Fernando; Gogatishvili, Amiran; Opic, Bohumír; Pick, Luboš 2 2013 On a theorem of Muckenhoupt-Wheeden in generalized Morrey spaces. Zbl 1250.42072Gogatishvili, A.; Mustafayev, R. 2 2011 Some new scales of characterization of Hardy’s inequality. Zbl 1193.26017Gogatishvili, Amiran; Kufner, Alois; Persson, Lars-Erik 2 2010 The \(\rho\)-quasiconcave functions and weighted inequalities. Zbl 1266.26037Evans, William Desmond; Gogatishvili, Amiran; Opic, Bohumír 2 2009 Fractional maximal functions in weighted Banach function spaces. Zbl 1015.42014Gogatishvili, Amiran 2 2000 Two-weight mixed inequalities in Orlicz classes for fractional maximal functions defined on homogeneous type spaces. Zbl 0881.42016Gogatishvili, A. 2 1997 Criteria of general weak type inequalities for integral transforms with positive kernels. Zbl 0802.42016Genebashvili, I.; Gogatishvili, A.; Kokilashvili, V. 2 1994 Riesz transforms and maximal functions in \(\Phi\) (L) classes. Zbl 0716.44004Gogatishvili, A. S. 2 1990 Characterization of embeddings of Sobolev-type spaces into generalized Hölder spaces defined by \(L^{p}\)-modulus of smoothness. Zbl 1407.26021Gogatishvili, Amiran; Neves, Júlio S.; Opic, Bohumír 1 2019 On the Rubio de Francia’s theorem in variable Lebesgue spaces. Zbl 1326.42023Gogatishvili, Amiran; Kopaliani, Tengiz 1 2014 Estimates for imaginary powers of Laplace operator in variable Lebesgue spaces and applications. Zbl 1319.42012Fiorenza, A.; Gogatishvili, A.; Kopaliani, T. 1 2014 Relations between some classes of functions of generalized bounded variation. Zbl 1307.42026Gogatishvili, Amiran; Goginava, Ushangi; Tephnadze, George 1 2014 Calderón-type theorems for operators of non-standard endpoint behaviour. Zbl 1184.46024Gogatishvili, Amiran; Pick, Luboš 1 2009 Some conditions characterizing the “reverse” Hardy inequality. Zbl 1170.26011Gogatishvili, A.; Kuliev, K.; Kulieva, G. 1 2008 Optimal embedding for Calderon type spaces and \(J\)-method spaces. Zbl 1453.46062Gogatishvili, A.; Ovchinnikov, V. I. 1 2006 A non-doubling Trudinger inequality. Zbl 1091.46019Gogatishvili, Amiran; Koskela, Pekka 1 2005 Criteria of two-weight inequalities for integral transformations with a positive kernel and maximal functions. Zbl 0909.42011Genebashvili, I. Z.; Gogatishvili, A. S.; Kokilashvili, V. M. 1 1996 Necessary and sufficient conditions for weighted Orlicz class inequalities for maximal functions and singular integrals. I. Zbl 0836.42012Gogatishvili, A.; Kokilashvili, V. 1 1995 Criteria of weight inequalities for integral transforms defined on homogeneous type spaces. Zbl 0863.42015Gogatishvili, A.; Kokilashvili, V. 1 1994 Weak type weighted inequalities for maximal functions with respect to the general basis. Zbl 0858.42009Gogatishvili, A. S. 1 1992 Maximal functions in the classes \(\varphi{} (L)\). Zbl 0755.42011Gogatishvili, A. S.; Kokilashvili, V. M.; Krbec, M. 1 1990 Some new results related to Lorentz \(G\Gamma\)-spaces and interpolation. Zbl 1442.46014Ahmed, Irshaad; Fiorenza, Alberto; Formica, Maria Rosaria; Gogatishvili, Amiran; Rakotoson, Jean Michel 2 2020 Characterization of embeddings of Sobolev-type spaces into generalized Hölder spaces defined by \(L^{p}\)-modulus of smoothness. Zbl 1407.26021Gogatishvili, Amiran; Neves, Júlio S.; Opic, Bohumír 1 2019 On grand and small Lebesgue and Sobolev spaces and some applications to PDE’s. Zbl 1398.46025Fiorenza, Alberto; Formica, Maria Rosaria; Gogatishvili, Amiran 10 2018 Characterization of interpolation between grand, small or classical Lebesgue spaces. Zbl 1409.46025Fiorenza, Alberto; Formica, Maria Rosaria; Gogatishvili, Amiran; Kopaliani, Tengiz; Rakotoson, Jean Michel 7 2018 Weak-type estimates in Morrey spaces for maximal commutator and commutator of maximal function. Zbl 1401.42018Gogatishvili, Amiran; Mustafayev, Rza; Aǧcayazi, Müjdat 4 2018 Construction of function spaces close to \(L^\infty \) with associate space close to \(L^1\). Zbl 1425.46017Edmunds, David; Gogatishvili, Amiran; Kopaliani, Tengiz 2 2018 Weighted iterated Hardy-type inequalities. Zbl 1375.26032Gogatishvili, Amiran; Mustafayev, Rza Ch. 13 2017 Embeddings of Lorentz-type spaces involving weighted integral means. Zbl 1383.46023Gogatishvili, Amiran; Křepela, Martin; Pick, Luboš; Soudský, Filip 6 2017 Iterated Hardy-type inequalities involving suprema. Zbl 1379.26018Gogatishvili, Amiran; Mustafayev, Rza Ch. 5 2017 Embeddings between weighted Copson and Cesàro function spaces. Zbl 06819576Gogatishvili, Amiran; Mustafayev, Rza; Ünver, Tuğçe 2 2017 Characterizations of Besov and Triebel-Lizorkin spaces via averages on balls. Zbl 1331.46023Dai, Feng; Gogatishvili, Amiran; Yang, Dachun; Yuan, Wen 10 2016 Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces. Zbl 1432.46013Caetano, António; Gogatishvili, Amiran; Opic, Bohumír 4 2016 A note on boundedness of the Hardy-Littlewood maximal operator on Morrey spaces. Zbl 1346.42017Gogatishvili, A.; Mustafayev, R. Ch. 3 2016 A note on maximal commutators and commutators of maximal functions. Zbl 1330.42012Agcayazi, Mujdat; Gogatishvili, Amiran; Koca, Kerim; Mustafayev, Rza 16 2015 Characterizations of Sobolev spaces via averages on balls. Zbl 1346.46023Dai, Feng; Gogatishvili, Amiran; Yang, Dachun; Yuan, Wen 10 2015 Characterization of associate spaces of generalized weighted weak-Lorentz spaces and embeddings. Zbl 1361.46022Gogatishvili, Amiran; Aykol, Canay; Guliyev, Vagif S. 3 2015 Embeddings of Sobolev-type spaces into generalized Hölder spaces involving \(k\)-modulus of smoothness. Zbl 1318.26045Gogatishvili, Amiran; Moura, Susana D.; Neves, Júlio S.; Opic, Bohumír 3 2015 Ulyanov-type inequalities between Lorentz-Zygmund spaces. Zbl 1316.41010Gogatishvili, Amiran; Opic, Bohumír; Tikhonov, Sergey; Trebels, Walter 10 2014 Characterization of associate spaces of weighted Lorentz spaces with applications. Zbl 1325.46032Gogatishvili, Amiran; Pick, Luboš; Soudský, Filip 8 2014 The rearrangement-invariant space \(\Gamma _{p,\phi}\). Zbl 1311.46025Gogatishvili, Amiran; Kerman, Ron 5 2014 Local Hardy-Littlewood maximal operator in variable Lebesgue spaces. Zbl 1285.42018Gogatishvili, A.; Danelia, A.; Kopaliani, T. 4 2014 Some scales of equivalent conditions to characterize the Stieltjes inequality: the case \(q<p\). Zbl 1298.26052Gogatishvili, Amiran; Persson, Lars-Erik; Stepanov, Vladimir D.; Wall, Peter 3 2014 On the Rubio de Francia’s theorem in variable Lebesgue spaces. Zbl 1326.42023Gogatishvili, Amiran; Kopaliani, Tengiz 1 2014 Estimates for imaginary powers of Laplace operator in variable Lebesgue spaces and applications. Zbl 1319.42012Fiorenza, A.; Gogatishvili, A.; Kopaliani, T. 1 2014 Relations between some classes of functions of generalized bounded variation. Zbl 1307.42026Gogatishvili, Amiran; Goginava, Ushangi; Tephnadze, George 1 2014 Reduction theorems for weighted integral inequalities on the cone of monotone functions. Zbl 1288.26018Gogatishvili, A.; Stepanov, V. D. 34 2013 Characterizations of Besov and Triebel-Lizorkin spaces on metric measure spaces. Zbl 1278.42029Gogatishvili, Amiran; Koskela, Pekka; Zhou, Yuan 32 2013 New pre-dual space of Morrey space. Zbl 1263.46031Gogatishvili, A.; Mustafayev, R. Ch. 17 2013 Reduction theorems for operators on the cones of monotone functions. Zbl 1326.47063Gogatishvili, Amiran; Stepanov, Vladimir D. 16 2013 Some new iterated Hardy-type inequalities: the case \({\theta=1}\). Zbl 1297.26035Gogatishvili, Amiran; Mustafayev, Rza; Persson, Lars-Erik 8 2013 Boundedness of Stein’s spherical maximal function in variable Lebesgue spaces and application to the wave equation. Zbl 1267.42019Fiorenza, Alberto; Gogatishvili, Amiran; Kopaliani, Tengiz 3 2013 The weighted Stieltjes inequality and applications. Zbl 1268.26026Gogatishvili, Amiran; Kufner, Alois; Persson, Lars-Erik 3 2013 Interpolation of uniformly absolutely continuous operators. Zbl 1273.46011Cobos, Fernando; Gogatishvili, Amiran; Opic, Bohumír; Pick, Luboš 2 2013 Some new iterated Hardy-type inequalities. Zbl 1260.26023Gogatishvili, A.; Mustafayev, R. Ch.; Persson, L.-E. 13 2012 Equivalence of norms of Riesz potential and fractional maximal function in generalized Morrey spaces. Zbl 1258.42017Gogatishvili, Amiran; Mustafayev, Rza 4 2012 Integral operators on cones of monotone functions. Zbl 1281.26014Gogatishvili, A.; Stepanov, V. D. 4 2012 Characterization of a rearrangement-invariant hull of a Besov space via interpolation. Zbl 1357.46030Gogatishvili, Amiran; Pick, Luboš; Schneider, Jan 3 2012 On scales of equivalent conditions characterizing weighted Stieltjes inequality. Zbl 1261.42005Gogatishvili, A.; Persson, L.-E.; Stepanov, V. D.; Wall, P. 3 2012 Integral operators on cones of monotone functions. Zbl 1263.47057Gogatishvili, A.; Stepanov, V. D. 3 2012 Boundedness of the Riesz potential in local Morrey-type spaces. Zbl 1223.42008Burenkov, Victor I.; Gogatishvili, Amiran; Guliyev, Vagif S.; Mustafayev, Rza Ch. 32 2011 Embeddings and the growth envelope of Besov spaces involving only slowly varying smoothness. Zbl 1238.46024Caetano, António M.; Gogatishvili, Amiran; Opic, Bohumír 9 2011 Dual spaces of local Morrey-type spaces. Zbl 1249.46020Gogatishvili, Amiran; Mustafayev, Rza 8 2011 Compact embeddings of Bessel-potential-type spaces into generalized Hölder spaces involving \(k\)-modulus of smoothness. Zbl 1213.46029Gogatishvili, Amiran; Neves, Júlio S.; Opic, Bohumír 7 2011 Compact embeddings of Besov spaces involving only slowly varying smoothness. Zbl 1249.46026Caetano, A.; Gogatishvili, A.; Opic, B. 3 2011 On a theorem of Muckenhoupt-Wheeden in generalized Morrey spaces. Zbl 1250.42072Gogatishvili, A.; Mustafayev, R. 2 2011 Boundedness of the fractional maximal operator in local Morrey-type spaces. Zbl 1207.42015Burenkov, V. I.; Gogatishvili, A.; Guliyev, V. S.; Mustafayev, R. Ch. 56 2010 Interpolation properties of Besov spaces defined on metric spaces. Zbl 1195.46033Gogatishvili, Amiran; Koskela, Pekka; Shanmugalingam, Nageswari 25 2010 Optimal embeddings of Bessel-potential-type spaces into generalized Hölder spaces involving \(k\)-modulus of smoothness. Zbl 1197.46017Gogatishvili, Amiran; Neves, Júlio S.; Opic, Bohumír 9 2010 Sharp estimates of the \(k\)-modulus of smoothness of Bessel potentials. Zbl 1194.26026Gogatishvili, Amiran; Neves, Júlio S.; Opic, Bohumír 7 2010 Some new scales of characterization of Hardy’s inequality. Zbl 1193.26017Gogatishvili, Amiran; Kufner, Alois; Persson, Lars-Erik 2 2010 Some new scales of weight characterizations of the class \(B_p\). Zbl 1199.26057Gogatishvili, A.; Kufner, A.; Persson, L.-E. 9 2009 Optimal embeddings and compact embeddings of Bessel-potential-type spaces. Zbl 1179.46029Gogatishvili, Amiran; Neves, Júlio S.; Opic, Bohumír 7 2009 The \(\rho\)-quasiconcave functions and weighted inequalities. Zbl 1266.26037Evans, William Desmond; Gogatishvili, Amiran; Opic, Bohumír 2 2009 Calderón-type theorems for operators of non-standard endpoint behaviour. Zbl 1184.46024Gogatishvili, Amiran; Pick, Luboš 1 2009 Weighted inequalities involving two Hardy operators with applications to embeddings of function spaces. Zbl 1150.26001Carro, María; Gogatishvili, Amiran; Martín, Joaquim; Pick, Luboš 19 2008 Sharp embeddings of Besov spaces involving only logarithmic smoothness. Zbl 1161.46017Caetano, António M.; Gogatishvili, Amiran; Opic, Bohumir 17 2008 The reverse Hardy inequality with measures. Zbl 1136.26004Evans, W. Desmond; Gogatishvili, Amiran; Opic, Bohumír 5 2008 Some conditions characterizing the “reverse” Hardy inequality. Zbl 1170.26011Gogatishvili, A.; Kuliev, K.; Kulieva, G. 1 2008 A reduction theorem for supremum operators. Zbl 1127.26012Gogatishvili, Amiran; Pick, Luboš 18 2007 Characterisation of embeddings in Lorentz spaces. Zbl 1128.26012Gogatishvili, A.; Johansson, M.; Okpoti, C. A.; Persson, L.-E. 10 2007 Sharpness and non-compactness of embeddings of Bessel-potential-type spaces. Zbl 1137.46020Gogatishvili, Amiran; Neves, Júlio Severino; Opic, Bohumír 6 2007 Interpolation orbits and optimal Sobolev’s embeddings. Zbl 1137.46021Gogatishvili, Amiran; Ovchinnikov, Vladimir I. 4 2007 Weighted inequalities for Hardy-type operators involving suprema. Zbl 1116.47041Gogatishvili, Amiran; Opic, Bohumír; Pick, Luboš 31 2006 Embeddings and duality theorem for weak classical Lorentz spaces. Zbl 1106.26018Gogatishvili, Amiran; Pick, Luboš 16 2006 Optimal embedding for Calderon type spaces and \(J\)-method spaces. Zbl 1453.46062Gogatishvili, A.; Ovchinnikov, V. I. 1 2006 Limiting reiteration for real interpolation with slowly varying functions. Zbl 1080.46012Gogatishvili, Amiran; Opic, Bohumír; Trebels, Walter 40 2005 Functional properties of rearrangement invariant spaces defined in terms of oscillations. Zbl 1110.46012Carro, María J.; Gogatishvili, Amiran; Martín, Joaquim; Pick, Luboš 17 2005 Optimality of embeddings of Bessel-potential-type spaces into generalized Hölder spaces. Zbl 1096.46016Gogatishvili, Amiran; Neves, Júlio S.; Opic, Bohumír 5 2005 A non-doubling Trudinger inequality. Zbl 1091.46019Gogatishvili, Amiran; Koskela, Pekka 1 2005 An equivalence theorem for integral conditions related to Hardy’s inequality. Zbl 1070.26015Gogatishvili, Amiram; Kufner, Alois; Persson, Lars-Erik; Wedestig, Anna 18 2004 Optimality of embeddings of Bessel-potential-type spaces into Lorentz-Karamata spaces. Zbl 1076.46021Gogatishvili, Amiran; Opic, Bohumír; Neves, Júlio S. 8 2004 Discretization and anti-discretization of rearrangement-invariant norms. Zbl 1066.46023Gogatishvili, Amiran; Pick, Luboš 37 2003 Duality principles and reduction theorems. Zbl 0985.46013Gogatishvili, Amiran; Pick, Luboš 8 2000 Fractional maximal functions in weighted Banach function spaces. Zbl 1015.42014Gogatishvili, Amiran 2 2000 The generalized Hardy operator with kernel and variable integral limits in Banach function spaces. Zbl 0947.47020Gogatishvili, A.; Lang, J. 24 1999 Weight theory for integral transforms on spaces of homogeneous type. Zbl 0955.42001Genebashvili, I.; Gogatishvili, A.; Kokilashvili, V.; Krbec, M. 56 1998 Two-weight mixed inequalities in Orlicz classes for fractional maximal functions defined on homogeneous type spaces. Zbl 0881.42016Gogatishvili, A. 2 1997 Solution of two-weight problems for integral transforms with positive kernels. Zbl 1056.42507Genebashvili, I.; Gogatishvili, A.; Kokilashvili, V. 6 1996 Criteria of strong type two-weighted inequalities for fractional maximal functions. Zbl 0884.42015Gogatishvili, A.; Kokilashvili, V. 4 1996 Criteria of two-weight inequalities for integral transformations with a positive kernel and maximal functions. Zbl 0909.42011Genebashvili, I. Z.; Gogatishvili, A. S.; Kokilashvili, V. M. 1 1996 Necessary and sufficient conditions for weighted Orlicz class inequalities for maximal functions and singular integrals. I. Zbl 0836.42012Gogatishvili, A.; Kokilashvili, V. 1 1995 Criteria of weighted inequalities in Orlicz classes for maximal functions defined on homogeneous type spaces. Zbl 0819.42007Gogatishvili, A.; Kokilashvili, V. 6 1994 Criteria of general weak type inequalities for integral transforms with positive kernels. Zbl 0802.42016Genebashvili, I.; Gogatishvili, A.; Kokilashvili, V. 2 1994 Criteria of weight inequalities for integral transforms defined on homogeneous type spaces. Zbl 0863.42015Gogatishvili, A.; Kokilashvili, V. 1 1994 Criteria of general weak type inequalities for integral transforms with positive kernels. Zbl 0803.42011Genebashvili, I.; Gogatishvili, A.; Kokilashvili, V. 6 1993 Weak and extra-weak type inequalities for the maximal operator and the Hilbert transform. Zbl 0798.42009Gogatishvili, Amiran; Pick, Luboš 5 1993 Maximal functions, \(\varphi(L)\) classes and Carleson measures. Zbl 0815.42010Gogatishvili, A.; Kokilashvili, V.; Krbec, M. 4 1993 Solutions of some weight problems. Zbl 0806.46031Genebashvili, Ioseb; Gogatishvili, Amiran; Kokilashvili, Vakhtang 3 1993 General weak type inequalities for the maximal operators and singular integrals. Zbl 0790.42008Gogatishvili, A. 3 1992 Weak type weighted inequalities for maximal functions with respect to the general basis. Zbl 0858.42009Gogatishvili, A. S. 1 1992 Riesz transforms and maximal functions in \(\Phi\) (L) classes. Zbl 0716.44004Gogatishvili, A. S. 2 1990 Maximal functions in the classes \(\varphi{} (L)\). Zbl 0755.42011Gogatishvili, A. S.; Kokilashvili, V. M.; Krbec, M. 1 1990 all cited Publications top 5 cited Publications all top 5 Cited by 426 Authors 52 Gogatishvili, Amiran 39 Guliyev, Vagif Sabir 29 Stepanov, Vladimir Dmitrievich 16 Opic, Bohumír 16 Sawano, Yoshihiro 15 Mizuta, Yoshihiro 15 Pick, Luboš 15 Shambilova, Guldarya Ermakovna 15 Shimomura, Tetsu 14 Persson, Lars-Erik 14 Yang, Dachun 13 Cobos, Fernando 13 Gol’dman, Mikhail L’vovich 13 Mustafayev, Rza Ch. 12 Fiorenza, Alberto 12 Kokilashvili, Vakhtang Mikhailovich 12 Yuan, Wen 11 Neves, Júlio Severino 11 Samko, Stefan Grigorievich 10 Ohno, Takao 10 Prokhorov, Dmitriĭ Vladimirovich 9 Deringoz, Fatih 9 Křepela, Martin 8 Cianchi, Andrea 8 Dominguez, Oscar 8 Haroske, Dorothee D. 8 Heikkinen, Toni 8 Ho, Kwok-Pun 8 Tuominen, Heli 7 Ahmed, Irshaad 7 Tikhonov, Sergey Yur’evich 6 Besov, Oleg Vladimirovich 6 Burenkov, Viktor Ivanovich 6 Fernández-Martínez, Pedro 6 Hasanov, Javanshir J. 6 Hasanov, Sabir G. 6 Koskela, Pekka 6 Meskhi, Alexander 6 Serbetci, Ayhan 6 Ushakova, Elena Pavlovna 6 Zhou, Yuan 5 Edmunds, David Eric 5 Kinnunen, Juha 5 Kopaliani, Tengiz 5 Maligranda, Lech 5 Domingues de Moura, Susana 5 Shanmugalingam, Nageswari 5 Soto, Tomás 5 Wheeden, Richard Lee 5 Zhang, Pu 4 Alberico, Angela 4 Caetano, António M. 4 Doktorski, Leo R. Ya. 4 Karadzhov, Georgi Eremiev 4 Karlovich, Alexeĭ Yur’evich 4 Nekvinda, Aleš 4 Oĭnarov, Ryskul Oĭnarovich 4 Omarova, Mehriban N. 4 Rakotoson, Jean-Michel 4 Sbordone, Carlo 4 Signes, Teresa M. 3 Akgun, Ramazan 3 Almeida, Alexandre 3 Aykol, Canay 3 Badalov, Xayyam A. 3 Bernardis, Ana L. 3 Fernández-Cabrera, Luz M. 3 Formica, Maria Rosaria 3 Franchi, Bruno 3 Gorbachëv, Dmitriĭ Viktorovich 3 Gurbuz, Ferit 3 Hakim, Denny Ivanal 3 Jain, Pankaj 3 Karaman, Turhan 3 Kufner, Alois 3 Kühn, Thomas 3 Malysheva, A. V. 3 Mammadov, Yagub Y. 3 Martín-Reyes, Francisco Javier 3 Matsuoka, Katsuo 3 Mehmood, Qaisar 3 Nakai, Eiichi 3 Nuutinen, Juho 3 Okpoti, Christopher Adjei 3 Ortega Salvador, Pedro 3 Rosenthal, Marcel 3 Saksman, Eero 3 Sinnamon, Gord 3 Soudský, Filip 3 Sun, Hongyan 3 Tanaka, Hitoshi 3 Tang, Tao 3 Trebels, Walter 3 Triebel, Hans 2 Aimar, Hugo A. 2 Akbulut, Ali 2 Aliev, Seymur S. 2 Alonso-Ruiz, Patricia 2 Asif, Muhammad 2 Astashkin, Sergeĭ Vladimir ...and 326 more Authors all top 5 Cited in 128 Serials 38 Journal of Mathematical Analysis and Applications 21 Doklady Mathematics 18 Mathematische Nachrichten 14 Journal of Functional Analysis 12 Journal of Function Spaces 11 Journal of Approximation Theory 11 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 11 Potential Analysis 10 Zeitschrift für Analysis und ihre Anwendungen 10 Georgian Mathematical Journal 10 The Journal of Fourier Analysis and Applications 10 Journal of Inequalities and Applications 10 Complex Variables and Elliptic Equations 9 Proceedings of the American Mathematical Society 9 Mediterranean Journal of Mathematics 9 Eurasian Mathematical Journal 8 Mathematical Notes 8 Mathematical Inequalities & Applications 8 Proceedings of the Steklov Institute of Mathematics 7 Siberian Mathematical Journal 7 Transactions of the American Mathematical Society 7 Revista Matemática Complutense 7 Acta Mathematica Sinica. English Series 6 Czechoslovak Mathematical Journal 6 Positivity 6 Banach Journal of Mathematical Analysis 6 Analysis and Mathematical Physics 5 Studia Mathematica 5 Collectanea Mathematica 5 Journal of Mathematical Sciences (New York) 5 Annales Academiae Scientiarum Fennicae. Mathematica 5 Journal of Function Spaces and Applications 4 Integral Equations and Operator Theory 4 The Journal of Geometric Analysis 4 Annals of Functional Analysis 3 Analysis Mathematica 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Journal of Computational and Applied Mathematics 3 Mathematische Annalen 3 Constructive Approximation 3 Forum Mathematicum 3 Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences 2 Indian Journal of Pure & Applied Mathematics 2 Russian Mathematical Surveys 2 Arkiv för Matematik 2 Annales Polonici Mathematici 2 Archiv der Mathematik 2 Canadian Mathematical Bulletin 2 Indiana University Mathematics Journal 2 Journal of Differential Equations 2 Manuscripta Mathematica 2 Mathematische Zeitschrift 2 Real Analysis Exchange 2 Results in Mathematics 2 Acta Mathematica Hungarica 2 Publicacions Matemàtiques 2 Journal of Integral Equations and Applications 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Bulletin des Sciences Mathématiques 2 Integral Transforms and Special Functions 2 Boletín de la Sociedad Matemática Mexicana. Third Series 2 Communications in Contemporary Mathematics 2 Portugaliae Mathematica. Nova Série 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Journal of Fixed Point Theory and Applications 2 Frontiers of Mathematics in China 2 Journal of Mathematical Inequalities 2 Tbilisi Mathematical Journal 2 Science China. Mathematics 2 Journal of Pseudo-Differential Operators and Applications 2 Kyoto Journal of Mathematics 2 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 2 Analysis and Geometry in Metric Spaces 1 Bulletin of the Australian Mathematical Society 1 Computers & Mathematics with Applications 1 Journal d’Analyse Mathématique 1 Mathematics of Computation 1 Advances in Mathematics 1 Annales de l’Institut Fourier 1 Canadian Journal of Mathematics 1 Demonstratio Mathematica 1 Functiones et Approximatio. Commentarii Mathematici 1 Glasgow Mathematical Journal 1 Journal of Optimization Theory and Applications 1 Journal für die Reine und Angewandte Mathematik 1 Mathematica Slovaca 1 Monatshefte für Mathematik 1 Osaka Journal of Mathematics 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Quaestiones Mathematicae 1 Revista de la Unión Matemática Argentina 1 Tohoku Mathematical Journal. Second Series 1 Tokyo Journal of Mathematics 1 Acta Applicandae Mathematicae 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Applied Numerical Mathematics 1 Journal of Scientific Computing 1 Applied Mathematical Modelling 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série ...and 28 more Serials all top 5 Cited in 22 Fields 294 Functional analysis (46-XX) 202 Harmonic analysis on Euclidean spaces (42-XX) 121 Real functions (26-XX) 107 Operator theory (47-XX) 31 Functions of a complex variable (30-XX) 27 Potential theory (31-XX) 27 Partial differential equations (35-XX) 23 Approximations and expansions (41-XX) 19 Abstract harmonic analysis (43-XX) 18 Integral equations (45-XX) 10 Integral transforms, operational calculus (44-XX) 10 Numerical analysis (65-XX) 5 Measure and integration (28-XX) 5 Ordinary differential equations (34-XX) 4 Topological groups, Lie groups (22-XX) 3 Probability theory and stochastic processes (60-XX) 2 Special functions (33-XX) 1 Combinatorics (05-XX) 1 Difference and functional equations (39-XX) 1 Convex and discrete geometry (52-XX) 1 Quantum theory (81-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year