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Pointwise multipliers on BMO spaces with non-doubling measures. (English) Zbl 1401.42009

Summary: Let \(\mu\) be a non-negative Radon measure satisfying the polynomial growth condition. In this paper, the authors characterize the set of pointwise multipliers on a BMO type space \(\mathrm{RBMO}(\mu)\) introduced by Tolsa.

MSC:

42B15 Multipliers for harmonic analysis in several variables
42B35 Function spaces arising in harmonic analysis
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References:

[1] S. Bloom, Pointwise multipliers of weighted BMO spaces, Proc. Amer. Math. Soc. 105 (1989), no. 4, 950–960. · Zbl 0706.42015 · doi:10.1090/S0002-9939-1989-0960640-3
[2] T. A. Bui and X. T. Duong, Hardy spaces, regularized BMO spaces and the boundedness of Calderón-Zygmund operators on non-homogeneous spaces, J. Geom. Anal. 23 (2013), no. 2, 895–932. · Zbl 1267.42013 · doi:10.1007/s12220-011-9268-y
[3] L. Diening, Maximal function on Musielak-Orlicz spaces and generalized Lebesgue spaces, Bull. Sci. Math. 129 (2005), no. 8, 657–700. · Zbl 1096.46013 · doi:10.1016/j.bulsci.2003.10.003
[4] X. Fu, H. Lin, D. Yang and D. Yang, Hardy spaces \(H^p\) over non-homogeneous metric measure spaces and their applications, Sci. China Math. 58 (2015), no. 2, 309–388. · Zbl 1311.42054 · doi:10.1007/s11425-014-4956-2
[5] G. Hu, Y. Meng and D. Yang, Multilinear commutators of singular integrals with non doubling measures, Integral Equations Operator Theory 51 (2005), no. 2, 235–255. · Zbl 1088.47028 · doi:10.1007/s00020-003-1251-y
[6] G. Hu, D. Yang and D. Yang, A new characterization of \(\operatorname{RBMO}(μ)\) by John-Strömberg sharp maximal functions, Czechoslovak Math. J. 59 (134) (2009), no. 1, 159–171.
[7] T. Hytönen, A framework for non-homogeneous analysis on metric spaces, and the RBMO space of Tolsa, Publ. Mat. 54 (2010), no. 2, 485–504.
[8] T. Hytönen, D. Yang and D. Yang, The Hardy space \(H^1\) on non-homogeneous metric spaces, Math. Proc. Cambridge Philos. Soc. 153 (2012), no. 1, 9–31.
[9] S. Janson, On functions with conditions on the mean oscillation, Ark. Mat. 14 (1976), no. 2, 189–196. · Zbl 0341.43005 · doi:10.1007/BF02385834
[10] A. K. Lerner, Some remarks on the Hardy-Littlewood maximal function on variable \(L^p\) spaces, Math. Z. 251 (2005), no. 3, 509–521. · Zbl 1092.42009 · doi:10.1007/s00209-005-0818-5
[11] H. Lin and D. Yang, Pointwise multipliers for localized Morrey-Campanato spaces on RD-spaces, Acta Math. Sci. Ser. B Engl. Ed. 34 (2014), no. 6, 1677–1694. · Zbl 1340.42022
[12] L. Liu and D. Yang, Pointwise multipliers for Campanato spaces on Gauss measure spaces, Nagoya Math. J. 214 (2014), 169–193. · Zbl 1293.42011 · doi:10.1215/00277630-2647739
[13] E. Nakai, Pointwise multipliers for functions of weighted bounded mean oscillation, Studia Math. 105 (1993), no. 2, 105–119. · Zbl 0812.42008 · doi:10.4064/sm-105-2-105-119
[14] ——–, Hardy-Littlewood maximal operator, singular integral operators and the Riesz potentials on generalized Morrey spaces, Math. Nachr. 166 (1994), 95–103. · Zbl 0837.42008 · doi:10.1002/mana.19941660108
[15] ——–, Pointwise multipliers, Memoirs of the Akashi College of Technology 37 (1995), 85–94.
[16] ——–, Pointwise multipliers on weighted BMO spaces, Studia Math. 125 (1997), no. 1, 35–56. · Zbl 0874.42009 · doi:10.4064/sm-125-1-35-56
[17] ——–, A generalization of Hardy spaces \(H^p\) by using atoms, Acta Math. Sin. (Engl. Ser.) 24 (2008), no. 8, 1243–1268. · Zbl 1153.42011 · doi:10.1007/s10114-008-7626-x
[18] E. Nakai and G. Sadasue, Pointwise multipliers on martingale Campanato spaces, Studia Math. 220 (2014), no. 1, 87–100. · Zbl 1301.46010 · doi:10.4064/sm220-1-5
[19] E. Nakai and K. Yabuta, Pointwise multipliers for functions of bounded mean oscillation, J. Math. Soc. Japan 37 (1985), no. 2, 207–218. · Zbl 0546.42019 · doi:10.2969/jmsj/03720207
[20] ——–, Pointwise multipliers for functions of weighted bounded mean oscillation on spaces of homogeneous type, Math. Japon. 46 (1997), no. 1, 15–28. · Zbl 0884.42010
[21] D. A. Stegenga, Bounded Toeplitz operators on \(H^1\) and applications of the duality between \(H^1\) and the functions of bounded mean oscillation, Amer. J. Math. 98 (1976), no. 3, 573–589. · Zbl 0335.47018 · doi:10.2307/2373807
[22] X. Tolsa, \(\operatorname{BMO}\), \(H^1\), and Calderón-Zygmund operators for non doubling measures, Math. Ann. 319 (2001), no. 1, 89–149.
[23] ——–, The space \(H^1\) for nondoubling measures in terms of a grand maximal operator, Trans. Amer. Math. Soc. 355 (2003), no. 1, 315–348. · Zbl 1021.42010 · doi:10.1090/S0002-9947-02-03131-8
[24] K. Yabuta, Pointwise multipliers of weighted BMO spaces, Proc. Amer. Math. Soc. 117 (1993), no. 3, 737–744. · Zbl 0779.42006 · doi:10.1090/S0002-9939-1993-1123671-X
[25] D. Yang and D. Yang, BMO-estimates for maximal operators via approximations of the identity with non-doubling measures, Canad. J. Math. 62 (2010), no. 6, 1419–1434. · Zbl 1206.42026 · doi:10.4153/CJM-2010-065-7
[26] D. Yang, D. Yang and G. Hu, The Hardy Space \(H^1\) with Non-doubling Measures and Their Applications, Lecture Notes in Mathematics 2084, Springer, Cham, 2013. · Zbl 1316.42002
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