Acta Mathematica Sinica, English Series

, Volume 33, Issue 11, pp 1443–1462 | Cite as

Multilinear singular integral operators with generalized kernels and their multilinear commutators

Article

Abstract

In this paper, the authors study a class of multilinear singular integral operators with generalized kernels and their multilinear commutators with BMO functions. By establishing the sharp maximal estimates, the boundedness on product of weighted Lebesgue spaces and product of variable exponent Lebesgue spaces is obtained, respectively. Moreover, the endpoint estimate of this class of mutilinear singular integral operators is also established. These results can improve the corresponding known results of classical multilinear Calderón–Zygmund operators and multilinear Calderón–Zygmund operators with Dini type kernels.

Keywords

Multilinear singular integral sharp maximal function multilinear commutator BMO function 

MR(2010) Subject Classification

42B20 42B35 

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Notes

Acknowledgements

We thank the referees for their time and comments.

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.School of SciencesChina University of Mining and TechnologyBeijingP. R. China
  2. 2.Department of Mathematical SciencesBall State UniversityMuncieUSA

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