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Weighted sharp boundedness for multilinear commutators

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Abstract

We obtain sharp estimates for some multilinear commutators related to certain sublinear integral operators. These operators include the Littlewood-Paley operator and Marcinkiewicz operator. As an application, we obtain weighted L p (p > 1) inequalities and an L log L-type estimate for multilinear commutators.

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References

  1. R. Coifman and Y. Meyer, “Wavelets, Calderón-Zygmund and multilinear operators,” Cambridge Stud. Adv. Math., 48 (1997).

  2. C. Pérez and R. Trujillo-Gonzalez, “Sharp weighted estimates for multilinear commutators,” J. London Math. Soc., 65, 672–692 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  3. J. Garcia-Cuerva and J. L. Rubio de Francia, “Weighted norm inequalities and related topics,” North-Holland Math., 16 (1985).

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

    Article  MATH  MathSciNet  Google Scholar 

  5. C. Pérez and G. Pradolini, “Sharp weighted endpoint estimates for commutators of singular integral operators,” Mich. Math. J., 49, 23–37 (2001).

    Article  MATH  Google Scholar 

  6. A. Torchinsky, “The real variable methods in harmonic analysis,” Pure Appl. Math., 123 (1986).

  7. A. Torchinsky and S. Wang, “A note on the Marcinkiewicz integral,” Colloq. Math., 60/61, 235–240 (1990).

    MathSciNet  Google Scholar 

  8. J. Alvarez, R. J. Bagby, D. S. Kurtz, and C. Pérez, “Weighted estimates for commutators of linear operators,” Stud. Math., 104, 194–209 (1993).

    Google Scholar 

  9. R. Coifman, R. Rochberg, and G. Weiss, “Factorization theorems for Hardy spaces in several variables,” Ann. Math., 103, 611–635 (1976).

    Article  MathSciNet  Google Scholar 

  10. L. Z. Liu, “Weighted weak type estimates for commutators of Littlewood-Paley operator,” Jpn. J. Math., 29, No. 1, 1–13 (2003).

    Google Scholar 

  11. L. Z. Liu and S. Z. Lu, “Weighted weak type inequalities for maximal commutators of Bochner-Riesz operator,” Hokkaido Math. J., 32, No. 1, 85–99 (2003).

    MATH  MathSciNet  Google Scholar 

  12. C. Pérez, “Sharp estimates for commutators of singular integrals via iterations of the Hardy-Littlewood maximal function,” J. Funct. Anal. Appl., 3, 743–756 (1997).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Hunan University, Changsha, China

    H. Xu, J. Zeng & L. Liu

Authors
  1. H. Xu
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  2. J. Zeng
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  3. L. Liu
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Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 10, pp. 1419–1431, October, 2007.

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Xu, H., Zeng, J. & Liu, L. Weighted sharp boundedness for multilinear commutators. Ukr Math J 59, 1591–1605 (2007). https://doi.org/10.1007/s11253-008-0006-y

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  • DOI: https://doi.org/10.1007/s11253-008-0006-y

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