Skip to main content
Log in

Weighted Lipschitz Estimates for Multilinear Commutator of Multiplier Operator

  • Published:
Vietnam Journal of Mathematics Aims and scope Submit manuscript

Abstract

In this paper, the weighted boundedness for the multilinear commutator of the multiplier operator associated to the weighted Lipschitz functions are obtained.

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

Access this article

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. Bloom, S.: A commutator theorem and weighted BMO. Trans. Am. Math. Soc. 292, 103–122 (1985)

    Article  MATH  Google Scholar 

  2. Chanillo, S.: A note on commutators. Indiana Univ. Math. J. 31, 7–16 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chen, W.G.: A Besov estimate for multilinear singular integrals. Acta Math. Sin. 16, 613–626 (2000)

    Article  MATH  Google Scholar 

  4. Zhang, P., Chen, J.C.: The \((L^{p},\dot{F}_{p}^{\beta,\infty})\)-boundedness of commutators of multipliers. Acta Math. Sin. Engl. Ser. 21, 765–772 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Garcia-Cuerva, J.: Weighted H p spaces. In: Dissert. Math, Warszawa, vol. 162 (1979)

    Google Scholar 

  6. Garcia-Cuerva, J., Rubio de Francia, J.L.: Weighted norm inequalities and related topics. In: North-Holland Math, Amsterdam, vol. 116 (1985)

    Google Scholar 

  7. Hu, B., Gu, J.: Necessary and sufficient conditions for boundedness of some commutators with weighted Lipschitz spaces. J. Math. Anal. Appl. 340, 598–605 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Janson, S.: Mean oscillation and commutators of singular integral operators. Ark. Mat. 16, 263–270 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kurtz, D.S., Wheeden, R.L.: Results on weighted norm inequalities for multipliers. Trans. Am. Math. Soc. 255, 343–362 (1979)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  11. Pérez, C., Trujillo-Gonzalez, R.: Sharp weighted estimates for multilinear commutators. J. Lond. Math. Soc. 65, 672–692 (2002)

    Article  MATH  Google Scholar 

  12. Stein, E.M.: Harmonic Analysis: Real Variable Methods, Orthogonality and Oscillatory Integrals. Princeton University Press, Princeton (1993)

    MATH  Google Scholar 

  13. Zhang, P., Chen, J.C.: The \((L^{p},\dot{F}_{p}^{\beta,\infty})\)-boundedness of commutators of multipliers. Acta Math. Sin. 21, 765–772 (2005)

    Article  MATH  Google Scholar 

  14. Zhang, P., Chen, J.C.: Boundedness properties for commutators of multipliers. Acta Math. Sin., China Ser. 49, 1387–1396 (2006)

    MATH  Google Scholar 

  15. You, Z.: Results of commutators obtained norm inequalities. Adv. Math. 17, 79–84 (1988)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Lanzhe Liu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhu, X., Liu, L. Weighted Lipschitz Estimates for Multilinear Commutator of Multiplier Operator. Viet J Math 41, 255–267 (2013). https://doi.org/10.1007/s10013-013-0018-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10013-013-0018-2

Keywords

Mathematics Subject Classification (2010)

Navigation