Skip to main content
SpringerLink
Log in

Commutators of multipliers on Hardy spaces

  • Published:
Analysis in Theory and Applications

Abstract

Let T be the multiplier operator associated to a multiplier m, and [b,T] be the commutator generated by T and a BMO function b. In this paper, the authors have proved that [b, T] is bounded from the Hardy spaceH 1(ℝn) into the weakL 1(ℝn) space and from certain atomic Hardy spaceH 1 b (ℝn into the Lebesgue spaceL 1(ℝn), when the multiplier m satisfies the conditions of Hörmander type.

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.

Similar content being viewed by others

References

  1. Alvarez, J., Continuity Properties for Linear Commutators of Calderón-Zygmund Operators, Collect. Math., 49(1998), 17–31.

    MathSciNet  Google Scholar 

  2. Alvarez, J., Bagby, R. J., Kurts, D. K. and Pérez, C., Weighted Estimates for Commutators of Linear Operators, 104:2(1993), 195–209.

    MATH  Google Scholar 

  3. Chen, J. C. and Zhang, P., Boundedness Properties for Commutators of Multiplier Operator, Manuscript.

  4. Chen, W. G. and Hu, G., Weak Type (H 1,L 1) Estimates for a Multilinear Singular Integral Operator, Adv. in Math. (China), 30:1(2001), 63–69.

    MATH  MathSciNet  Google Scholar 

  5. Hörmander, L., Estimates for Translation Invariant Operators inL p-Spaces, Acta Math., 104(1960), 93–139.

    Article  MATH  MathSciNet  Google Scholar 

  6. Kurtz, D. S., and Wheeden, R. L., Results on Weighted Norm Inequalities for Multipliers, Trans. Amer. Math. Soc., 255(1979), 343–362.

    Article  MATH  MathSciNet  Google Scholar 

  7. Lu, S. Z., Four Lectures on RealH p Spaces, New York, Singapore: World Scientific Publishing Co Pte Ltd, 1995.

    Google Scholar 

  8. Paluszyński, M., Characterization of the Besov Spaces via the Commutator Operator of Coifman, Rochberg and Weiss, Indiana Univ. Math. J., 44:1(1995), 1–17.

    MathSciNet  Google Scholar 

  9. Pérez, C., Endpoint Estimates for Commutators of Singular Integral Operators, J. Funct. Anal., 128(1995), 163–185.

    Article  MATH  MathSciNet  Google Scholar 

  10. Stein, E. M., Singular Integral and Differentiability Properties of Functions, Princeton N J: Princeton Univ. Press, 1970

    Google Scholar 

  11. Stein, E. M., Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton N J: Princeton Univ. Press, 1993.

    MATH  Google Scholar 

  12. Strömberg, J. O. and Torkinsky, A., Weighted Hardy Spaces, In: Lecture Notes in Math., Vol. 1381. Springer-Verlag, 1989

  13. You, Z., Results of Commutators Obtained from Weighted Norm Inequalities, Adv. in Math. (China), 171(1988), 79–84. In Chinese.

    MATH  Google Scholar 

  14. Zhang, P. and Chen, J. C., The (L p,F β,∞ p )-Boundedness of Commutators of Multipliers, Acta Math. Sinica (English Series), to appear.

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Zhejiang Sci-Tech University, 310018, Hangzhou, P. R. China

    Pu Zhang

  2. Department of Computational Science, Zhejiang Gongshang University, 310035, Hangzhou, P. R. China

    Jiukun Hua

Authors
  1. Pu Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jiukun Hua
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported by the Research Funds of Zhejiang Sci-Tech University (No. 0313055-Y).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, P., Hua, J. Commutators of multipliers on Hardy spaces. Anal. Theory Appl. 21, 226–234 (2005). https://doi.org/10.1007/BF02836952

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02836952

Key words

AMS(2000) subject classification

Search

Navigation