Asekritova, I.; Kruglyak, N.; Mastyło, M. Stability of the inverses of interpolated operators with application to the Stokes system. (English) Zbl 1517.46018 Rev. Mat. Complut. 36, No. 1, 163-206 (2023). MSC: 46B70 47A13 35Q30 PDFBibTeX XMLCite \textit{I. Asekritova} et al., Rev. Mat. Complut. 36, No. 1, 163--206 (2023; Zbl 1517.46018) Full Text: DOI
Asekritova, I.; Kruglyak, N.; Mastyło, M. Stability of Fredholm properties on interpolation Banach spaces. (English) Zbl 1467.46017 J. Approx. Theory 260, Article ID 105493, 28 p. (2020). MSC: 46B70 47A53 PDFBibTeX XMLCite \textit{I. Asekritova} et al., J. Approx. Theory 260, Article ID 105493, 28 p. (2020; Zbl 1467.46017) Full Text: DOI
Asekritova, Irina; Kruglyak, Natan; Mastyło, Mieczysław A unified approach to compatibility theorems on invertible interpolated operators. arXiv:2008.00449 Preprint, arXiv:2008.00449 [math.FA] (2020). MSC: 46B70 47A13 BibTeX Cite \textit{I. Asekritova} et al., ``A unified approach to compatibility theorems on invertible interpolated operators'', Preprint, arXiv:2008.00449 [math.FA] (2020) Full Text: arXiv OA License
Asekritova, Irina; Karlovich, Yuri; Kruglyak, Natan One-sided invertibility of discrete operators and their applications. (English) Zbl 1417.39068 Aequationes Math. 92, No. 1, 39-73 (2018). MSC: 39A70 39B32 41A05 46B70 47B38 47B39 PDFBibTeX XMLCite \textit{I. Asekritova} et al., Aequationes Math. 92, No. 1, 39--73 (2018; Zbl 1417.39068) Full Text: DOI
Kruglyak, Natan; Setterqvist, Eric Invariant \(K\)-minimal sets in the discrete and continuous settings. (English) Zbl 1379.46021 J. Fourier Anal. Appl. 23, No. 3, 572-611 (2017). MSC: 46B70 46E30 46N10 PDFBibTeX XMLCite \textit{N. Kruglyak} and \textit{E. Setterqvist}, J. Fourier Anal. Appl. 23, No. 3, 572--611 (2017; Zbl 1379.46021) Full Text: DOI
Asekritova, I.; Kruglyak, N.; Mastyło, M. Interpolation of Fredholm operators. (English) Zbl 1364.46020 Adv. Math. 295, 421-496 (2016). Reviewer: Cătălin Badea (Villeneuve d’Ascq) MSC: 46B70 47A53 PDFBibTeX XMLCite \textit{I. Asekritova} et al., Adv. Math. 295, 421--496 (2016; Zbl 1364.46020) Full Text: DOI arXiv
Kruglyak, Natan; Setterqvist, Eric Discrete taut strings and real interpolation. (English) Zbl 1390.46022 J. Funct. Anal. 270, No. 2, 671-704 (2016). MSC: 46B70 46E30 46N10 PDFBibTeX XMLCite \textit{N. Kruglyak} and \textit{E. Setterqvist}, J. Funct. Anal. 270, No. 2, 671--704 (2016; Zbl 1390.46022) Full Text: DOI Link
Kruglyak, Natan; Niyobuhungiro, Japhet Subdifferentiability of infimal convolution on Banach couples. (English) Zbl 1394.46015 Funct. Approximatio, Comment. Math. 52, No. 2, 311-326 (2015). MSC: 46B70 46E35 PDFBibTeX XMLCite \textit{N. Kruglyak} and \textit{J. Niyobuhungiro}, Funct. Approximatio, Comment. Math. 52, No. 2, 311--326 (2015; Zbl 1394.46015) Full Text: DOI Euclid
Asekritova, Irina; Cobos, Fernando; Kruglyak, Natan Interpolation of closed subspaces and invertibility of operators. (English) Zbl 1329.46022 Z. Anal. Anwend. 34, No. 1, 1-15 (2015). Reviewer: Nacib Gurgel Albuquerque (João Pessoa) MSC: 46B70 46E35 PDFBibTeX XMLCite \textit{I. Asekritova} et al., Z. Anal. Anwend. 34, No. 1, 1--15 (2015; Zbl 1329.46022) Full Text: DOI
Kruglyak, Natan; Niyobuhungiro, Japhet Characterization of optimal decompositions in real interpolation. (English) Zbl 1300.41002 J. Approx. Theory 185, 1-11 (2014). Reviewer: Costica Mustăţa (Cluj-Napoca) MSC: 41A05 46B70 46B45 46N10 47N10 PDFBibTeX XMLCite \textit{N. Kruglyak} and \textit{J. Niyobuhungiro}, J. Approx. Theory 185, 1--11 (2014; Zbl 1300.41002) Full Text: DOI
Asekritova, Irina; Kruglyak, Natan Necessary and sufficient conditions for invertibility of operators in spaces of real interpolation. (English) Zbl 1279.46012 J. Funct. Anal. 264, No. 1, 207-245 (2013). Reviewer: Nicolae Popa (Bucureşti) MSC: 46B70 PDFBibTeX XMLCite \textit{I. Asekritova} and \textit{N. Kruglyak}, J. Funct. Anal. 264, No. 1, 207--245 (2013; Zbl 1279.46012) Full Text: DOI
Kislyakov, Sergei; Kruglyak, Natan Extremal problems in interpolation theory, Whitney-Besicovitch coverings, and singular integrals. (English) Zbl 1270.46003 Monografie Matematyczne. Instytut Matematyczny PAN (New Series) 74. Basel: Birkhäuser/Springer (ISBN 978-3-0348-0468-4/hbk; 978-3-0348-0469-1/ebook). x, 316 p. (2013). Reviewer: Manfred Tasche (Rostock) MSC: 46-02 46B70 46E30 46E35 42B20 42B35 PDFBibTeX XMLCite \textit{S. Kislyakov} and \textit{N. Kruglyak}, Extremal problems in interpolation theory, Whitney-Besicovitch coverings, and singular integrals. Basel: Birkhäuser/Springer (2013; Zbl 1270.46003) Full Text: DOI
Asekritova, Irina; Cerdà, Joan; Kruglyak, Natan The Riesz-Herz equivalence for capacitary maximal functions. (English) Zbl 1281.42017 Rev. Mat. Complut. 25, No. 1, 43-59 (2012). Reviewer: Petr Gurka (Praha) MSC: 42B25 46B70 PDFBibTeX XMLCite \textit{I. Asekritova} et al., Rev. Mat. Complut. 25, No. 1, 43--59 (2012; Zbl 1281.42017) Full Text: DOI
Asekritova, Irina; Kruglyak, Natan Invertibility of operators in spaces of real interpolation. (English) Zbl 1154.46009 Rev. Mat. Complut. 21, No. 1, 207-217 (2008). Reviewer: Georgi E. Karadzhov (Sofia) MSC: 46B70 46M35 PDFBibTeX XMLCite \textit{I. Asekritova} and \textit{N. Kruglyak}, Rev. Mat. Complut. 21, No. 1, 207--217 (2008; Zbl 1154.46009) Full Text: DOI EuDML
Kruglyak, Natan An elementary proof of the real version of the Riesz-Thorin theorem. (English) Zbl 1143.46305 De Carli, Laura (ed.) et al., Interpolation theory and applications. A conference in honor of Michael Cwikel on the occasion of his 59th birthday, March 29–31, 2006 and AMS special session on interpolation theory and applications, AMS sectional meeting, Miami, FL, USA, April 1–2, 2006. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4207-2/pbk). Contemporary Mathematics 445, 179-182 (2007). MSC: 46B70 46M35 PDFBibTeX XMLCite \textit{N. Kruglyak}, Contemp. Math. 445, 179--182 (2007; Zbl 1143.46305)
Kruglyak, Natan The \(K\)-functional and Calderón-Zygmund type decompositions. (English) Zbl 1142.46314 De Carli, Laura (ed.) et al., Interpolation theory and applications. A conference in honor of Michael Cwikel on the occasion of his 59th birthday, March 29–31, 2006 and AMS special session on interpolation theory and applications, AMS sectional meeting, Miami, FL, USA, April 1–2, 2006. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4207-2/pbk). Contemporary Mathematics 445, 183-194 (2007). MSC: 46B70 46M35 PDFBibTeX XMLCite \textit{N. Kruglyak}, Contemp. Math. 445, 183--194 (2007; Zbl 1142.46314)
Asekritova, I.; Kruglyak, N. Interpolation of Besov spaces in the nondiagonal case. (English. Russian original) Zbl 1144.46017 St. Petersbg. Math. J. 18, No. 4, 511-516 (2007); translation from Algebra Anal. 18, No. 4, 1-9 (2006). MSC: 46B70 46E35 46M35 PDFBibTeX XMLCite \textit{I. Asekritova} and \textit{N. Kruglyak}, St. Petersbg. Math. J. 18, No. 4, 511--516 (2007; Zbl 1144.46017); translation from Algebra Anal. 18, No. 4, 1--9 (2006) Full Text: DOI
Kruglyak, Natan Calderón–Zygmund type decompositions and applications. (English) Zbl 1122.46012 Proc. Est. Acad. Sci., Phys. Math. 55, No. 3, 170-173 (2006). MSC: 46B70 46E15 PDFBibTeX XMLCite \textit{N. Kruglyak}, Proc. Est. Acad. Sci., Phys. Math. 55, No. 3, 170--173 (2006; Zbl 1122.46012)
Kislyakov, S. V.; Kruglyak, N. Ya. Stability of approximation under the action of singular integral operators. (English. Russian original) Zbl 1123.46018 Funct. Anal. Appl. 40, No. 4, 285-297 (2006); translation from Funkts. Anal. Prilozh. 40, No. 4, 49-64 (2006). Reviewer: Georgi E. Karadzhov (Sofia) MSC: 46B70 42B20 PDFBibTeX XMLCite \textit{S. V. Kislyakov} and \textit{N. Ya. Kruglyak}, Funct. Anal. Appl. 40, No. 4, 285--297 (2006; Zbl 1123.46018); translation from Funkts. Anal. Prilozh. 40, No. 4, 49--64 (2006) Full Text: DOI
Asekritova, Irina; Krugljak, Natan; Nikolova, Ludmila The Lizorkin–Freitag formula for several weighted \(L_p\) spaces and vector-valued interpolation. (English) Zbl 1090.46013 Stud. Math. 170, No. 3, 227-239 (2005). Reviewer: Joan Cerdà (Barcelona) MSC: 46B70 46E30 PDFBibTeX XMLCite \textit{I. Asekritova} et al., Stud. Math. 170, No. 3, 227--239 (2005; Zbl 1090.46013) Full Text: DOI
Krugljak, N.; Sagher, Y.; Shvartsman, P. Weak-type operators and the strong fundamental lemma of real interpolation theory. (English) Zbl 1100.46014 Stud. Math. 170, No. 2, 173-201 (2005). MSC: 46B70 46M35 PDFBibTeX XMLCite \textit{N. Krugljak} et al., Stud. Math. 170, No. 2, 173--201 (2005; Zbl 1100.46014) Full Text: DOI
Asekritova, Irina; Krugljak, Natan Real interpolation of vector-valued spaces in non-diagonal case. (English) Zbl 1073.46013 Proc. Am. Math. Soc. 133, No. 6, 1665-1675 (2005). MSC: 46B70 46E30 PDFBibTeX XMLCite \textit{I. Asekritova} and \textit{N. Krugljak}, Proc. Am. Math. Soc. 133, No. 6, 1665--1675 (2005; Zbl 1073.46013) Full Text: DOI
Krugljak, Natan; Milman, Mario A distance between orbits that controls commutator estimates and invertibility of operators. (English) Zbl 1228.46068 Adv. Math. 182, No. 1, 78-123 (2004). MSC: 46M35 46B70 47B47 PDFBibTeX XMLCite \textit{N. Krugljak} and \textit{M. Milman}, Adv. Math. 182, No. 1, 78--123 (2004; Zbl 1228.46068) Full Text: DOI
Krugljak, Natan; Maligranda, Lech Calderón-Lozanovskiĭ construction on weighted Banach function lattices. (English) Zbl 1039.46018 J. Math. Anal. Appl. 288, No. 2, 744-757 (2003). MSC: 46B70 46E30 46B42 46M35 46E15 PDFBibTeX XMLCite \textit{N. Krugljak} and \textit{L. Maligranda}, J. Math. Anal. Appl. 288, No. 2, 744--757 (2003; Zbl 1039.46018) Full Text: DOI
Asekritova, Irina; Krugljak, Natan; Maligranda, Lech; Nikolova, Lyudmila; Persson, Lars-Erik Lions–Peetre reiteration formulas for triples and their applications. (English) Zbl 0987.46024 Stud. Math. 145, No. 3, 219-254 (2001). Reviewer: M.Turinici (Iaşi) MSC: 46B70 46M35 46E35 46E30 46E05 42C40 PDFBibTeX XMLCite \textit{I. Asekritova} et al., Stud. Math. 145, No. 3, 219--254 (2001; Zbl 0987.46024) Full Text: DOI
Krugljak, Natan; Maligranda, Lech; Persson, Lars-Erik The failure of the Hardy inequality and interpolation of intersections. (English) Zbl 1021.46024 Ark. Mat. 37, No. 2, 323-344 (1999). Reviewer: Eugene Tokarev (Kharkiv) MSC: 46E30 26D15 PDFBibTeX XMLCite \textit{N. Krugljak} et al., Ark. Mat. 37, No. 2, 323--344 (1999; Zbl 1021.46024) Full Text: DOI
Cerdà, Joan; Martín, Joaquim; Krugljak, Natan Ya. Commutators for approximation spaces and Marcinkiewicz-type multipliers. (English) Zbl 0953.41023 J. Approximation Theory 100, No. 2, 251-265 (1999). Reviewer: T.Precupanu (Iaşi) MSC: 41A65 46M35 47B38 PDFBibTeX XMLCite \textit{J. Cerdà} et al., J. Approx. Theory 100, No. 2, 251--265 (1999; Zbl 0953.41023) Full Text: DOI
Asekritova, Irina; Krugljak, Natan On equivalence of \(K\)- and \(J\)-methods for \((n+1)\)-tuples of Banach spaces. (English) Zbl 0901.46017 Stud. Math. 122, No. 2, 99-116 (1997). MSC: 46B70 46M35 PDFBibTeX XMLCite \textit{I. Asekritova} and \textit{N. Krugljak}, Stud. Math. 122, No. 2, 99--116 (1997; Zbl 0901.46017) Full Text: EuDML
Kruglyak, N. Ya. Piecewise polynomial approximation with free nodes and the \(F_\alpha\)-characteristic for \(\alpha\in[1-\frac 1n, 1)\). (English. Russian original) Zbl 0905.41010 St. Petersbg. Math. J. 9, No. 2, 225-237 (1998); translation from Algebra Anal. 9, No. 2, 58-72 (1997). Reviewer: Yuri A. Brudnyi (Haifa) MSC: 41A30 42B25 46E35 46B70 PDFBibTeX XMLCite \textit{N. Ya. Kruglyak}, St. Petersbg. Math. J. 9, No. 2, 1 (1997; Zbl 0905.41010); translation from Algebra Anal. 9, No. 2, 58--72 (1997)
Asekritova, Irina U.; Krugljak, Natan Ya.; Maligranda, Lech; Persson, Lars-Erik Distribution and rearrangement estimates of the maximal function and interpolation. (English) Zbl 0888.42011 Stud. Math. 124, No. 2, 107-132 (1997). Reviewer: K.Yabuta (Nara) MSC: 42B25 26D15 46E30 46M35 PDFBibTeX XMLCite \textit{I. U. Asekritova} et al., Stud. Math. 124, No. 2, 107--132 (1997; Zbl 0888.42011) Full Text: EuDML
Kruglyak, N. Ya. Smooth analogs of the Calderón-Zygmund decompositions, quantitative covering theorems and the \(K\)-functional for the couple \((L_ q,\dot W_ p^ k)\). (English. Russian original) Zbl 0885.46017 St. Petersbg. Math. J. 8, No. 4, 617-649 (1997); translation from Algebra Anal. 8, No. 4, 110-160 (1996). MSC: 46B70 46M35 46E35 PDFBibTeX XMLCite \textit{N. Ya. Kruglyak}, St. Petersbg. Math. J. 8, No. 4, 110--160 (1996; Zbl 0885.46017); translation from Algebra Anal. 8, No. 4, 110--160 (1996)
Cwikel, Michael; Krugljak, Natan; Mastyło, Mieczysław On complex interpolation of compact operators. (English) Zbl 0864.46011 Ill. J. Math. 40, No. 3, 353-364 (1996). Reviewer: J.Howard (Las Vegas/New Mexico) MSC: 46B70 46M35 47B07 PDFBibTeX XMLCite \textit{M. Cwikel} et al., Ill. J. Math. 40, No. 3, 353--364 (1996; Zbl 0864.46011)
Kruglyak, Natan Ya.; Maligranda, Lech; Persson, Lars Erik A Carlson type inequality with blocks and interpolation. (English) Zbl 0824.46088 Stud. Math. 104, No. 2, 161-180 (1993). MSC: 46M35 46E30 26D15 PDFBibTeX XMLCite \textit{N. Ya. Kruglyak} et al., Stud. Math. 104, No. 2, 161--180 (1993; Zbl 0824.46088) Full Text: DOI EuDML
Krugljak, Natan Ja. On the reiteration property of \(\vec X_{\varphi,q}\) spaces. (English) Zbl 0804.46085 Math. Scand. 73, No. 1, 65-80 (1993). MSC: 46M35 PDFBibTeX XMLCite \textit{N. Ja. Krugljak}, Math. Scand. 73, No. 1, 65--80 (1993; Zbl 0804.46085) Full Text: DOI EuDML
Brudnyĭ, Yu. A.; Krugljak, N. Ya. Interpolation functors and interpolation spaces. Vol. 1. (English) Zbl 0743.46082 North-Holland Mathematical Library. 47. Amsterdam etc.: North-Holland. xv, 718 p. (1991). Reviewer: M. Milman (Boca Raton) MSC: 46M35 46B70 46-02 PDFBibTeX XMLCite \textit{Yu. A. Brudnyĭ} and \textit{N. Ya. Krugljak}, Interpolation functors and interpolation spaces. Vol. 1. Amsterdam etc.: North-Holland (1991; Zbl 0743.46082)
Kruglyak, N. Ya; Mastyło, M. Correct interpolation functors of orbits. (English) Zbl 0826.46066 J. Funct. Anal. 102, No. 2, 401-413 (1991). MSC: 46M35 46B70 PDFBibTeX XMLCite \textit{N. Y. Kruglyak} and \textit{M. Mastyło}, J. Funct. Anal. 102, No. 2, 401--413 (1991; Zbl 0826.46066) Full Text: DOI
Kruglyak, N. Ja. A set of K-functionals for a mixed Banach couple. (English) Zbl 0825.46019 Function spaces, Proc. 2nd Int. Conf., Poznań/Pol. 1989, Teubner-Texte Math. 120, 248-251 (1991). MSC: 46M35 46B70 PDFBibTeX XMLCite \textit{N. Ja. Kruglyak}, in: Near convexity in Banach spaces. . 248--251 (1991; Zbl 0825.46019)
Kruglyak, N. Ya. On extension of the Calderon-Lozanovskiĭ operation to arbitrary Banach pairs. (Russian) Zbl 0770.46031 Issled. Teor. Funkts. Mnogikh Veshchestv. Perem. 1990, 77-90 (1990). MSC: 46M35 46B70 PDFBibTeX XMLCite \textit{N. Ya. Kruglyak}, Issled. Teor. Funkts. Mnogikh Veshchestv. Perem. 1990, 77--90 (1990; Zbl 0770.46031)
[Arazy, J.; Krugljak, N.; Milman, M.; Peetre, J.] Problem section. (English) Zbl 0549.46042 Interpolation spaces and allied topics in analysis, Proc. conf., Lund/Swed. 1983, Lect. Notes Math. 1070, 232-239 (1984). Reviewer: A.V.Bukhvalov MSC: 46M35 46-02 PDFBibTeX XML
Kruglyak, N. Ya. On the constant of K-divisibility of the pair (C,\(C^ 1)\). (Russian) Zbl 0501.46068 Issled. Teor. Funkts. Mnogikh Veshchestv. Perem. 1981, 37-44 (1981). MSC: 46M35 46E15 PDFBibTeX XMLCite \textit{N. Ya. Kruglyak}, Issled. Teor. Funkts. Mnogikh Veshchestv. Perem. 1981, 37--44 (1981; Zbl 0501.46068)
Brudnyj, Yu. A.; Kruglyak, N. Ya. Real interpolation functors. (English. Russian original) Zbl 0475.46052 Sov. Math., Dokl. 23, 5-8 (1981); translation from Dokl. Akad. Nauk SSSR 256, 14-17 (1981). MSC: 46M35 46E30 PDFBibTeX XMLCite \textit{Yu. A. Brudnyj} and \textit{N. Ya. Kruglyak}, Sov. Math., Dokl. 23, 5--8 (1981; Zbl 0475.46052); translation from Dokl. Akad. Nauk SSSR 256, 14--17 (1981)
Kruglyak, N. Ya. The Nash-Moser implicit function theorem and nonlinear interpolation. (Russian) Zbl 0447.58006 Studies in the theory of functions of several real variables, interuniv. thematic Work Collect., No. 1, Yaroslavl 1976, 55-65 (1976). MSC: 58C15 46M35 PDFBibTeX XML