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Multiple weighted estimates for commutators of multilinear maximal function

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Abstract

Let M be the multilinear maximal function and \(\vec b\) = (b 1,..., b m ) be a collection of locally integrable functions. Denote by M \(\vec b\) and \(\vec b\), M] the maximal commutator and the commutator of M with \(\vec b\), respectively. In this paper, the multiple weighted strong and weak type estimates for operators M \(\vec b\) and [\(\vec b\), M] are studied. Some characterizations of the class of functions b j are given, for which these operators satisfy some strong or weak type estimates.

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Authors and Affiliations

  1. Department of Mathematics, Mudanjiang Normal University, Mudanjiang, 157011, P. R. China

    Pu Zhang

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  1. Pu Zhang
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Correspondence to Pu Zhang.

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Supported by National Natural Science Foundation of China (Grant No. 11271162), the Scientific Research Fund of Heilongjiang Provincial Education Department (Grant No. 12531720) and the Scientific Research Fund of Mudanjiang Normal University (Grant No. GY201305)

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Zhang, P. Multiple weighted estimates for commutators of multilinear maximal function. Acta. Math. Sin.-English Ser. 31, 973–994 (2015). https://doi.org/10.1007/s10114-015-4293-6

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  • DOI: https://doi.org/10.1007/s10114-015-4293-6

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