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Weighted norm inequalities with general weights for the commutator of Calderón

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Abstract

In this paper, by a sharp function estimate and an idea of Lerner, the authors establish some weighted estimates for the m-multilinear integral operator which is bounded from L 1(ℝn)×…×L 1(ℝn) to L 1/m,∞(ℝn), and the associated kernel K(x; y 1, …, y m ) enjoys a regularity on the variable x. As an application, weighted estimates with general weights are given for the commutator of Calderón.

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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  MathSciNet  MATH  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 University Press, Princeton, 1986, 3–45

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  5. Lerner, A. K., Ombrosi, S., Pérez, C., et al.: New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory. Adv. in Math., 220, 1222–1264 (2009)

    Article  MATH  Google Scholar 

  6. Duong, X., Grafakos, L., Yan, L.: Multilinear operators with non-smooth kernels and commutators of singular integrals. Trans. Amer. Math. Soc., 362(4), 2089–2113 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  7. Duong, X., Gong, R., Grafakos, L., et al.: Maximal operators for multilinear singular integrals with nonsmooth kernels. Indiana Univ. Math. J., 58(6), 2517–2542 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. John, F.: Quasi-isometric Mappings, Seminar 1962–1963 di Analisi, Algebra, Geometria e Topologia, Roma, 1965

  9. Strömberg, J. O.: Bounded mean oscillation with Orlicz norm and duality of Hardy spaces. Indiana Univ. Math. J., 28, 511–544 (1979)

    Article  MathSciNet  Google Scholar 

  10. Lerner, A. K.: Weighted norm inequalities for the local sharp maximal function. J. Fourier Anal. Appl., 10, 645–674 (2004)

    Article  MathSciNet  Google Scholar 

  11. Carrozza, M., Passarelli Di Napoli, A.: Composition of maximal operators. Publ. Mat., 40, 397–409 (1996)

    MathSciNet  Google Scholar 

  12. Pérez, C.: On sufficient conditions for the boundedness of the Hardy-Littlewood maximal operator between weighted L p-spaces with different weights. Proc. London Math. Soc., 49, 135–157 (1995)

    Article  Google Scholar 

  13. Carro, M. J., Pérez, C., Soria, R., et al.: Maximal functions and the control of weighted inequalities for the fractional integral operator. Indiana Univ. Math. J., 54, 627–644 (2005)

    Article  MathSciNet  MATH  Google Scholar 

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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 Science, Nantong University, Nantong, 226007, P. R. China

    Yue Ping Zhu

Authors
  1. Guo En Hu
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  2. Yue Ping Zhu
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Correspondence to Guo En Hu or Yue Ping Zhu.

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Supported by National Natural Science Foundation of China (Grant No. 10971228)

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Hu, G.E., Zhu, Y.P. Weighted norm inequalities with general weights for the commutator of Calderón. Acta. Math. Sin.-English Ser. 29, 505–514 (2013). https://doi.org/10.1007/s10114-012-1352-0

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  • DOI: https://doi.org/10.1007/s10114-012-1352-0

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