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Multilinear Commutators of Singular Integral Operators in Variable Exponent Herz-Type Spaces

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Abstract

In this paper, we study the boundedness of multilinear commutators of Hardy–Littlewood maximal operators in variable exponent Herz and Herz–Morrey spaces, which in turn are used to obtain the boundedness for a large class of the multilinear commutators related to sublinear operators. Moreover, based on the atomic decomposition and on generalization of the BMO norm, we study the boundedness of multilinear commutators of singular integral operators with Calderón–Zygmund kernels in variable exponent Herz-type Hardy spaces.

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Acknowledgements

The authors would like to express their deep gratitude to the referees for pointing the reference [11] out to us and for giving many valuable comments and suggestions.

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Authors and Affiliations

  1. School of Mathematics and Physics, Anhui Polytechnic University, Wuhu, 241000, China

    Liwei Wang

  2. School of Mathematics and Computer Science, Anhui Normal University, Wuhu, 241003, China

    Lisheng Shu

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  1. Liwei Wang
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  2. Lisheng Shu
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Correspondence to Liwei Wang.

Additional information

Communicated by V. Ravichandran.

Liwei Wang was partly supported by a grant from the NNSF of China (No. 11471033).

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Wang, L., Shu, L. Multilinear Commutators of Singular Integral Operators in Variable Exponent Herz-Type Spaces. Bull. Malays. Math. Sci. Soc. 42, 1413–1432 (2019). https://doi.org/10.1007/s40840-017-0554-0

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  • DOI: https://doi.org/10.1007/s40840-017-0554-0

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