Taiwanese Journal of Mathematics

Pointwise Multipliers on BMO Spaces with Non-doubling Measures

Wei Li, Eiichi Nakai, and Dongyong Yang

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Abstract

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 $\operatorname{RBMO}(\mu)$ introduced by Tolsa.

Article information

Source
Taiwanese J. Math. (2017), 21 pages.

Dates
First available in Project Euclid: 17 August 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1502935225

Digital Object Identifier
doi:10.11650/tjm/8140

Subjects
Primary: 42B15: Multipliers
Secondary: 42B35: Function spaces arising in harmonic analysis

Keywords
BMO space multiplier non-doubling measure

Citation

Li, Wei; Nakai, Eiichi; Yang, Dongyong. Pointwise Multipliers on BMO Spaces with Non-doubling Measures. Taiwanese J. Math., advance publication, 17 August 2017. doi: 10.11650/tjm/8140. https://projecteuclid.org/euclid.twjm/1502935225


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References

  • S. Bloom, Pointwise multipliers of weighted BMO spaces, Proc. Amer. Math. Soc. 105 (1989), no. 4, 950–960.
  • 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.
  • L. Diening, Maximal function on Musielak-Orlicz spaces and generalized Lebesgue spaces, Bull. Sci. Math. 129 (2005), no. 8, 657–700.
  • 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.
  • 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.
  • G. Hu, D. Yang and D. Yang, A new characterization of $\operatorname{RBMO}(\mu)$ by John-Strömberg sharp maximal functions, Czechoslovak Math. J. 59 (134) (2009), no. 1, 159–171.
  • 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.
  • 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.
  • S. Janson, On functions with conditions on the mean oscillation, Ark. Mat. 14 (1976), no. 2, 189–196.
  • A. K. Lerner, Some remarks on the Hardy-Littlewood maximal function on variable $L^p$ spaces, Math. Z. 251 (2005), no. 3, 509–521.
  • 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.
  • L. Liu and D. Yang, Pointwise multipliers for Campanato spaces on Gauss measure spaces, Nagoya Math. J. 214 (2014), 169–193.
  • E. Nakai, Pointwise multipliers for functions of weighted bounded mean oscillation, Studia Math. 105 (1993), no. 2, 105–119.
  • ––––, Hardy-Littlewood maximal operator, singular integral operators and the Riesz potentials on generalized Morrey spaces, Math. Nachr. 166 (1994), 95–103.
  • ––––, Pointwise multipliers, Memoirs of the Akashi College of Technology 37 (1995), 85–94.
  • ––––, Pointwise multipliers on weighted BMO spaces, Studia Math. 125 (1997), no. 1, 35–56.
  • ––––, A generalization of Hardy spaces $H^p$ by using atoms, Acta Math. Sin. (Engl. Ser.) 24 (2008), no. 8, 1243–1268.
  • E. Nakai and G. Sadasue, Pointwise multipliers on martingale Campanato spaces, Studia Math. 220 (2014), no. 1, 87–100.
  • E. Nakai and K. Yabuta, Pointwise multipliers for functions of bounded mean oscillation, J. Math. Soc. Japan 37 (1985), no. 2, 207–218.
  • ––––, Pointwise multipliers for functions of weighted bounded mean oscillation on spaces of homogeneous type, Math. Japon. 46 (1997), no. 1, 15–28.
  • 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.
  • X. Tolsa, $\operatorname{BMO}$, $H^1$, and Calderón-Zygmund operators for non doubling measures, Math. Ann. 319 (2001), no. 1, 89–149.
  • ––––, The space $H^1$ for nondoubling measures in terms of a grand maximal operator, Trans. Amer. Math. Soc. 355 (2003), no. 1, 315–348.
  • K. Yabuta, Pointwise multipliers of weighted BMO spaces, Proc. Amer. Math. Soc. 117 (1993), no. 3, 737–744.
  • 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.
  • 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.