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Commutators of n-dimensional rough Hardy operators

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Abstract

In this paper, we study central BMO estimates for commutators of n-dimensional rough Hardy operators. Furthermore, λ-central BMO estimates for commutators on central Morrey spaces are discussed.

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References

  1. Alvarez J, Lakey J, Guzmán-Partida M. Spaces of bounded λ-central mean oscillation, Morrey spaces, and λ-central Carleson measures. Collect Math, 2000, 51: 1–47

    MATH  MathSciNet  Google Scholar 

  2. Anderson K, Muckenhoupt B. Weighted weak type inequalities with applications to Hilbert transforms and maximal functions. Studia Math, 1982, 72: 9–26

    MathSciNet  Google Scholar 

  3. Beurling A. Construction and analysis of some convolution algebras. Ann Inst Fourier (Grenoble), 1964, 14: 1–32

    MATH  MathSciNet  Google Scholar 

  4. Chen Y Z, Lau K S. On some new classes of Hardy spaces. J Funct Anal, 1989, 84: 255–278

    Article  MATH  MathSciNet  Google Scholar 

  5. Christ M, Grafakos L. Best constants for two nonconvolution inequalities. Proc Amer Math Soc, 1995, 123: 1687–1693

    MATH  MathSciNet  Google Scholar 

  6. Feichtinger H G. An elementary approach to Wiener’s third Tauberian theorem on the Euclidean n-space. Symposia Math, 1988, 29: 267–301

    Google Scholar 

  7. Fu Z W, Lin Y, Lu S Z. λ-central BMO estimates for commutators of singular integral operators with rough kernels. Acta Math Sin (Engl Ser), 2008, 24: 373–386

    Article  MATH  MathSciNet  Google Scholar 

  8. Fu Z W, Liu Z G, Lu S Z, et al. Characterization for commutators of n-dimensional fractional Hardy operators. Sci China Ser A, 2007, 10: 1418–1426

    Article  MathSciNet  Google Scholar 

  9. García-Cuerva J. Hardy spaces and Beurling algebras. J London Math Soc, 1989, 39: 499–513

    Article  MATH  MathSciNet  Google Scholar 

  10. Golubov B. Boundedness of the Hardy and the Hardy-Littlewood operators in the spaces ReH1 and BMO. Math Sb, 1997, 188: 1041–1054

    Article  MATH  MathSciNet  Google Scholar 

  11. Hardy G H. Note on a theorem of Hilbert. Math Z, 1920, 6: 314–317

    Article  MathSciNet  Google Scholar 

  12. Hardy G H, Littlewood J E, Pólya G. Inequalities, 2nd ed. Cambridge: Cambridge University Press, 1952

    MATH  Google Scholar 

  13. Komori Y. Notes on commutators on Herz-type spaces. Arch Math, 2003, 81: 318–326

    Article  MATH  MathSciNet  Google Scholar 

  14. Long S C, Wang J. Commutators of Hardy operators. J Math Anal Appl, 2002, 274: 626–644

    Article  MATH  MathSciNet  Google Scholar 

  15. Lu S Z, Ding Y, Yan D Y. Singular integrals and related topics. Singapore: World Scientific, 2007

    Book  MATH  Google Scholar 

  16. Lu S Z, Yang D C. The Littlewood-Paley function and φ-transform characterizations of a new Hardy space HK 2 associated with the Herz space. Studia Math, 1992, 101: 258–298

    MathSciNet  Google Scholar 

  17. Lu S Z, Yang D C. The central BMO spaces and Littewood-Paley operators. Approx Theory Appl, 1995, 11: 72–94

    MATH  MathSciNet  Google Scholar 

  18. Lu S Z, Yang D C. The decomposition of the weighted Herz spaces and its applications. Sci China Ser A, 1995, 38: 147–158

    MATH  MathSciNet  Google Scholar 

  19. Lu S Z, Yang D C. The local version of H p(ℝn) spaces at the origin. Studia Math, 1995, 116: 103–131

    MATH  MathSciNet  Google Scholar 

  20. Lu S Z, Yang D C. Some characterizations of weighted Herz-type Hardy spaces and its applications. Acta Math Sin (Engl Ser), 1997, 13: 45–58

    MATH  MathSciNet  Google Scholar 

  21. Sawyer E. Weighted Lebesgue and Lorentz norm inequalities for the Hardy operator. Trans Amer Math Soc, 1984, 281: 329–337

    Article  MATH  MathSciNet  Google Scholar 

  22. Wiener N. Generalized harmonic analysis. Acta Math, 1930, 55: 117–258

    Article  MATH  MathSciNet  Google Scholar 

  23. Wiener N. Tauberian theorems. Ann Math, 1932, 33: 1–100

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    ZunWei Fu, ShanZhen Lu & FaYou Zhao

  2. Department of Mathematics, Linyi University, Linyi, 276005, China

    ZunWei Fu

Authors
  1. ZunWei Fu
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  2. ShanZhen Lu
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  3. FaYou Zhao
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Correspondence to ShanZhen Lu.

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Fu, Z., Lu, S. & Zhao, F. Commutators of n-dimensional rough Hardy operators. Sci. China Math. 54, 95–104 (2011). https://doi.org/10.1007/s11425-010-4110-8

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  • DOI: https://doi.org/10.1007/s11425-010-4110-8

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