Skip to main content
SpringerLink
Log in

Weighted estimates for the multilinear commutators of the Littlewood-Paley operators

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

In this paper, weighted L p estimates and sharp weighted endpoint estimates for the multilinear commutators of the Littlewood-Paley operators are established.

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. Stein E M. On some functions of Littlewood-Paley and Zygmund. Bull Amer Math Soc, 67: 99–101: (1961)

    Article  MATH  MathSciNet  Google Scholar 

  2. Fefferman C. Inequalities for strongly singular convolution operators. Acta Math, 124: 9–36: (1970)

    Article  MATH  MathSciNet  Google Scholar 

  3. Torchinsky A. Real-Variable Methods in Harmonic Analysis. New York: Academic Press, 1986

    MATH  Google Scholar 

  4. Pérez C, Trujillo-Gonzá R. Sharp weighted estimates for multilinear commutators. J London Math Soc, 65 (2): 672–692: (2002)

    Article  MATH  MathSciNet  Google Scholar 

  5. Tolsa X. A proof of the weak (1,1) inequality for singular integrals with non-doubling measures based on a Calderon-Zygmund decomposition. Publ Mat, 45: 163–174: (2001)

    MATH  MathSciNet  Google Scholar 

  6. Hu G, Meng Y, Yang D. Multilinear commutators of singular integrals with non-doubling measures. Integral Equations Operator Theory, 51: 235–255: (2005)

    Article  MATH  MathSciNet  Google Scholar 

  7. Muckenhoupt B, Wheeden R. Norm inequalities for the Littlewood-Paley function g *λ . Trans Amer Math Soc, 191: 95–111: (1974)

    Article  MATH  MathSciNet  Google Scholar 

  8. Liu L. A sharp endpoint estimate for a mulitilinear Littlewood-Paley operators. Georgian Math J, 11: 361–370: (2004)

    MATH  MathSciNet  Google Scholar 

  9. Torchinsky A, Wang S. A note on the Marcinkiewicz integral. Colloq Math, 60–61: 235–243: (1990)

    MathSciNet  Google Scholar 

  10. Sakamoto M, Yabuta K. Boundedness of Marcinkiewicz functions. Studia Math, 135: 103.142: (1999)

    MathSciNet  Google Scholar 

  11. Pérez C. Endpoint estimate for commutators of singular integral operators. J Funct Anal, 128: 163–185: (1995)

    Article  MATH  MathSciNet  Google Scholar 

  12. Garcia-Cuerva J, Rubio de Francia J L. Weighted Norm Inequalities Related Topics. Amsterdam: North-Holland, 1985

    MATH  Google Scholar 

  13. Stein E M. Singular Integrals and Differentiability Properties of Functions. Princeton: Princeton University Press, 1970

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, China

    QingYing Xue & Yong Ding

Authors
  1. QingYing Xue
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yong Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to QingYing Xue.

Additional information

The first author was supported by National Natural Science Foundation of China (Grant No. 10701010) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry. The second author was supported by National Natural Science Foundation of China (Grant No. 10571015) and Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20050027025)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xue, Q., Ding, Y. Weighted estimates for the multilinear commutators of the Littlewood-Paley operators. Sci. China Ser. A-Math. 52, 1849–1868 (2009). https://doi.org/10.1007/s11425-009-0049-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-009-0049-z

Keywords

MSC(2000)

Search

Navigation