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Weighted Norm Inequalities with General Weights for the Commutator of Calderón 被引量：5

Weighted Norm Inequalities with General Weights for the Commutator of Calderón
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摘要 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 L1 （Rn） ×..…… L1 （Rn） to L1/m,∞（Rn）, and the associated kernel K（x; yl,.. , Ym） enjoys a regularity on the variable x. As an application, weighted estimates with general weights are given for the commutator of CalderSn. 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 L1 （Rn） ×..…… L1 （Rn） to L1/m,∞（Rn）, and the associated kernel K（x; yl,.. , Ym） enjoys a regularity on the variable x. As an application, weighted estimates with general weights are given for the commutator of CalderSn.
作者 Guo En HU Yue Ping ZHU
机构地区 Department of Applied Mathematics School of Science
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2013年第3期505-514,共10页 数学学报（英文版）
基金 Supported by National Natural Science Foundation of China (Grant No. 10971228)
关键词 Approximation to the identity weighted norm inequality singular integral operator max-imal operator non-smooth kernel Approximation to the identity, weighted norm inequality, singular integral operator, max-imal operator, non-smooth kernel
分类号 O178 [理学—基础数学]
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参考文献13

  • 1Coifman, R. R., Meyer, Y.: On commutators of singular integrals and bilinear singular integrals. Trans. Amer. Math. Soc., 212, 315-331 (1975).
  • 2Coifman, R. R., Meyer, Y.: Nonlinear Harmonic Analysis, Operator Theory and P. D. E. In: Beijing Lec- tures in Harmonic Analysis (Beijing, 1984), Ann. Math. Stud. 112, Princeton University Press, Princeton, 1986, 3-45.
  • 3Grafakos, L., Torres, R. H.: Maximal operators and weighted norm inequalities for multilinear singular integrals. Indiana Univ. Math. J., 51, 1261-1276 (2002).
  • 4Grafakos, L., Torres, R. H.: Multilinear Calder6n-Zygmund theory. Adv. in Math., 165, 124-164 (2002).
  • 5Lerner, A. K., Ombrosi, S., P@rez, C., et al.: New maximal functions and multiple weights for the multilinear CalderSn-Zygmund theory. Adv. in Math., 220, 1222-1264 (2009).
  • 6Duong, 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).
  • 7Duong, X., Gong, R., Grafakos, L., et al.: Maximal operators for multilinear singular integrals with non- smooth kernels. Indiana Univ. Math. J., 58(6), 2517-2542 (2009).
  • 8John, F.: Quasi-isometric Mappings, Seminar 1962-1963 di Analisi, Algebra, Geometria e Topologia, Roma, 1965.
  • 9StrSmberg, J. 0.: Bounded mean oscillation with Orlicz norm and duality of Hardy spaces. Indiana Univ. Math. J., 28, 511-544 (1979).
  • 10Lerner, A. K.: Weighted norm inequalities for the local sharp maximal function. J. Fourier Anal. Appl., 10, 645-674 (2004).

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Acta Mathematica Sinica,English Series
2013年 第3期

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