Skip to main content
SpringerLink
Log in

Multilinear Calderón-Zygmund operator on products of Hardy spaces

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

Abstract

In this paper, the authors establish the boundedness of the multilinear Calderón-Zygmund operator from products of Hardy spaces into Hardy spaces.

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., 212, 315–331 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  2. Coifman, R. R., Meyer, Y.: Nonlinear harmonic analysis, operator theory and P. D. E. In: Beijing Lectures in Harmonic Analysis (Beijing, 1984), Ann. Math. Stud. 112, Princeton Univ. Press, Princeton, NJ, 1986, 3–45

    Google Scholar 

  3. Grafakos, L., Torres, R.: Multilinear Calderón-Zygmund theory. Adv. Math., 165, 124–164 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  4. Grafakos, L., Kalton, N.: Multilinear Calderón-Zygmund operators on Hardy spaces. Collect. Math., 52, 169–179 (2001)

    MATH  MathSciNet  Google Scholar 

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

    MathSciNet  Google Scholar 

  6. Grafakos, L., Torres, R.: Maximal operator and weighted norm inequalities for multilinear singular integrals. Indiana Univ. Math. J., 51, 1261–1276 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  7. Lin, H., Meng, Y.: Maximal multilinear Calderón-Zygmund operators with non-doubling measures. Acta Math. Hungar., 124, 263–287 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  8. Lin, H., Meng, Y., Yang, D.: Weighted estimates for commutators of multilinear Calderón-Zygmund operators with non-doubling measures. Acta Math. Sci. Engl. Ser., 30, 1–18 (2010)

    MATH  MathSciNet  Google Scholar 

  9. Fefferman, C., Stein, E. M.: H p spaces of several variables. Acta Math., 129, 137–193 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  10. Coifman, R. R.: A real variable characterization of H p. Studia Math., 51, 269–274 (1974)

    MATH  MathSciNet  Google Scholar 

  11. Latter, R. H.: A decomposition of H p(ℝn) in terms of atoms. Studia Math., 62, 92–101 (1977)

    MathSciNet  Google Scholar 

  12. Meda, S., Sjögren, P., Vallarino, M.: On the H 1-L 1 boundedness of operators. Proc. Amer. Math. Soc., 136, 2921–2931 (2008)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, P. O. Box 1001-747, Zhengzhou, 450002, P. R. China

    Guo En Hu

  2. School of Information, Renmin University of China, Beijing, 100872, P. R. China

    Yan Meng

Authors
  1. Guo En Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yan Meng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yan Meng.

Additional information

The first author is supported by National Natural Science Foundation of China (Grant No. 10971228); the second author is supported by National Natural Science Foundation of China (Grant No. 11071200)

Electronic supplementary material

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hu, G.E., Meng, Y. Multilinear Calderón-Zygmund operator on products of Hardy spaces. Acta. Math. Sin.-English Ser. 28, 281–294 (2012). https://doi.org/10.1007/s10114-012-0240-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-012-0240-y

Keywords

MR(2000) Subject Classification

Search

Navigation