Skip to main content
SpringerLink
Log in

Weighted estimates for the multilinear singular integral operators with non-smooth kernels

  • Articles
  • Published:
Science China Mathematics Aims and scope Submit manuscript

Abstract

In this paper, by sharp function estimates and certain weak type endpoint estimates, the authors establish some weighted norm inequalities with A p weights for the multilinear singular integral operators with non-smooth kernels.

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. Coifman R R, Meyer Y. On commutators of singular integrals and bilinear singular integrals. Trans Amer Math Soc, 1975, 212: 315–331

    Article  MathSciNet  MATH  Google Scholar 

  2. Coifman R R, Meyer Y. Nonlinear harmonic analysis, operator theory and PDE. In: Beijing Lectures in Harmonic Analysis, Ann Math Stud 112. Princeton, NJ: Princeton University Press, 1986, 3–45

    Google Scholar 

  3. Duong X, Gong R, Grafakos L, et al. Maximal operators for multilinear singular integrals with non-smooth kernels. Indiana Univ Math J, 2009, 58: 2517–2542

    Article  MathSciNet  MATH  Google Scholar 

  4. Duong X, Grafakos L, Yan L. Multilinear operators with non-smooth kernels and commutators of singular integrals. Trans Amer Math Soc, 2010, 362: 2089–2113

    Article  MathSciNet  MATH  Google Scholar 

  5. Duong X, McIntosh A. Singular integral operators with non-smooth kernels on irregular domains. Rev Mat Iberoamericana, 1999, 15: 233–265

    MathSciNet  MATH  Google Scholar 

  6. García-Cuerva J, Rubio de Francia J L. Weighted Norm Inequalities and Related Topics. Amsterdam: North-Holland Publishing Co., 1985

    MATH  Google Scholar 

  7. Grafakos L, Kalton N. Multilinear Calderón-Zymunnd operators on Hardy spaces. Collect Math, 2001, 52: 169–179

    MathSciNet  MATH  Google Scholar 

  8. Grafakos L, Kalton N. Some remarks on multilinear maps and interpolation. Math Ann, 2001, 319: 151–180

    Article  MathSciNet  MATH  Google Scholar 

  9. Grafakos L, Torres R H. Multilinear Calderón-Zygmund theory. Adv Math, 2002, 165: 124–164

    Article  MathSciNet  MATH  Google Scholar 

  10. Grafakos L, Torres R H. Maximal operators and weighted norm inequalities for multilinear singular integrals. Indiana Univ Math J, 2002, 51: 1261–1276

    Article  MathSciNet  MATH  Google Scholar 

  11. Grafakos L, Torres R H. On multilinear singular integrals of Calderón-Zygmund type. Publ Mat, 2002, Extra: 57–91

  12. Hu G. Weighted norm inequalities for the multilinear Calderón-Zygmund operators. Sci China Math, 2010, 53: 1863–1876

    Article  MathSciNet  MATH  Google Scholar 

  13. Kenig C, Stein E M. Multilinear estimates and fractional integral integration. Math Res Lett, 1999, 6: 1–15

    MathSciNet  MATH  Google Scholar 

  14. Lerner A K, Ombrosi S, Pérez C, et al. New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory. Adv Math, 2009, 220: 1222–1264

    Article  MathSciNet  MATH  Google Scholar 

  15. Martell J M. Sharp maximal functions associated with approximations of the identity in spaces of homogeneous type and applications. Studia Math, 2004, 161: 113–145

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou, 450002, China

    GuoEn Hu

  2. Department of Mathematics, Beijing Normal University, Beijing, 100875, China

    ShanZhen Lu

Authors
  1. GuoEn Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. ShanZhen Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to GuoEn Hu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hu, G., Lu, S. Weighted estimates for the multilinear singular integral operators with non-smooth kernels. Sci. China Math. 54, 587–602 (2011). https://doi.org/10.1007/s11425-010-4135-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-010-4135-z

Keywords

MSC(2000)

Search

Navigation