Skip to main content
SpringerLink
Log in

Weighted estimates for commutators of strongly singular Calderón–Zygmund operators

  • Published:
Acta Mathematica Sinica, English Series Aims and scope Submit manuscript

Abstract

In this paper, the authors establish the boundedness of commutators generated by strongly singular Calderón–Zygmund operators and weighted BMO functions on weighted Herz-type Hardy spaces. Moreover, the corresponding results for commutators generated by strongly singular Calderón–Zygmund operators and weighted Lipschitz functions can also be obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Alvarez, J., Milman, M.: Hp continuity properties of Calderón–Zygmund type operators. J. Math. Anal. Appl., 118, 63–79 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  2. Alvarez, J., Milman, M.: Vector valued inequalities for strongly singular Calderón–Zygmund operators. Rev. Mat. Iberoamericana, 2, 405–426 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  3. Coifman, R.: A real variable characterization of Hp. Studia Math., 51, 269–274 (1974)

    MathSciNet  MATH  Google Scholar 

  4. Fefferman, C., Stein, E. M.: Hp spaces of several variable. Acta Math., 129, 137–193 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  5. Garcia-Cuerva, J.: Weighted Hp spaces. Dissertationes Math., 162, 1–63 (1979)

    MathSciNet  Google Scholar 

  6. Garcia-Cuerva, J., de Francia, J. R.: Weighted Norm Inequalities and Related Topics, North-Holland, Amsterdam, The Netherlands, 1985

    MATH  Google Scholar 

  7. Hu, G. E., Zhu, Y. P.: Weighted norm inequalities with general weights for the commutator of Calderón. Acta Math. Sin., Engl. Ser., 29, 505–514 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. Jiang, Y. S., Tang, L., Yang, D. C.: Continuity of commutators on weighted Herz-type spaces. Kyushu J. Math., 53, 245–263 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  9. Journé, J. L.: Calderón operators, pseudo-differential operators and the Cauchy integral of Calderón. Lecture Notes in Math., 994, 1–127 (1983)

    Article  MATH  Google Scholar 

  10. Kong, X. B., Jiang, Y. S., Zhang, L.: The boundedmess of commutators with the weighted Lipschitz functions. Acta Math. Sci. Ser. A Chin. Ed., 33A(1), 152–164 (2013)

    MathSciNet  MATH  Google Scholar 

  11. Li, J. F., Lu, S. Z.: Strongly singular integral operators on weighted Hardy spaces. Acta Math. Sin., Engl. Ser., 22, 767–772 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  12. Li, K. W., Sun, W. C.: Weighted estimates for multilinear pseudodifferential operators. Acta Math. Sin., Engl. Ser., 30, 1281–1288 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  13. Lin, Y.: Strongly singular Calderón–Zygmund operator and commutator on Morrey type spaces. Acta Math. Sin., Engl. Ser., 23, 2097–2110 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  14. Lin, Y., Liu, Z. G., Cong, W. L.: Weighted Lipschitz estimates for commutators on weighted Morrey spaces. J. Inequal. Appl., 338, 19 pages (2015)

    MathSciNet  MATH  Google Scholar 

  15. Lin, Y., Lu, S. Z.: Strongly singular Calderón–Zygmund operators and their commutators. Jordan J. Math. Stat., 1, 31–49 (2008)

    MATH  Google Scholar 

  16. Lin, Y., Lu, S. Z.: Boundedness of commutators on Hardy-type spaces. Integral Equ. Oper. Theory, 57, 381–396 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  17. Lin, Y., Sun, G. F.: Strongly singular Calderón–Zygmund operators and commutators on weighted Morrey spaces. J. Inequal. Appl., 519, 15 pages (2014)

    MathSciNet  Google Scholar 

  18. Lin, Y., Xu, M.: Endpoint estimates for Marcinkiewicz integrals on weighted weak Hardy spaces. Acta Math. Sin., Engl. Ser., 31, 430–444 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  19. Lin, Y., Zhang, M. M.: Weighted BMO estimates for Toeplitz operators on weighted Lebesgue spaces. J. Funct. Spaces, 349535, 10 pages (2015)

    MathSciNet  MATH  Google Scholar 

  20. Lu, G. Z., Zhang, P.: Multilinear Calderón–Zygmund operators with kernels of Dini’s type and applications. Nonlinear Anal., 107, 92–117 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  21. Lu, G. Z., Zhu, Y. P.: Singular integrals and weighted Triebel–Lizorkin and Besov spaces of arbitrary number of parameters. Acta Math. Sin., Engl. Ser., 29, 39–52 (2013)

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  23. Lu, S. Z., Yang, D. C.: The weighted Herz-type Hardy space and its applications. Sci. China Ser. A, 38, 662–673 (1995)

    MathSciNet  MATH  Google Scholar 

  24. Muckenhoupt, B.: Weighted norm inequalities for the Hardy maximal function. Trans. Amer. Math. Soc., 165, 207–226 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  25. Paluszyński, M.: Characterization of the Besov spaces via the commutator operator of Coifman, Rochberg and Weiss. Indiana Univ. Math. J., 44, 1–17 (1995)

    MathSciNet  MATH  Google Scholar 

  26. Shi, S. G.: Estimates for vector-valued commutators on weighted Morrey space and applications. Acta Math. Sin., Engl. Ser., 29, 883–896 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  27. Wheeden, R. L.: A characterization of some weighted norm inequalities for the fractional maximal function. Studia Math., 107, 257–272 (1993)

    MathSciNet  MATH  Google Scholar 

  28. Zhang, P.: Multiple weighted estimates for commutators of multilinear maximal function. Acta Math. Sin., Engl. Ser., 31, 973–994 (2015)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Sciences, China University of Mining and Technology, Beijing, 100083, P. R. China

    Yan Lin & Guo Ming Zhang

Authors
  1. Yan Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guo Ming Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yan Lin.

Additional information

Supported by National Natural Science Foundation of China (Grant No. 11171345), the Fundamental Research Funds for the Central Universities (Grant No. 2009QS16) and the State Scholarship Fund of China

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lin, Y., Zhang, G.M. Weighted estimates for commutators of strongly singular Calderón–Zygmund operators. Acta. Math. Sin.-English Ser. 32, 1297–1311 (2016). https://doi.org/10.1007/s10114-016-6154-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-016-6154-3

Keywords

MR(2010) Subject Classification

Search

Navigation