Multiple weighted estimates for multilinear commutators of multilinear singular integrals with generalized kernels

Liwen Gao; Yan Lin; Shuhui Yang

doi:10.4134/JKMS.j210768

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2024; 61(2): 207-226

Online first article February 15, 2024 Printed March 1, 2024

https://doi.org/10.4134/JKMS.j210768

Multiple weighted estimates for multilinear commutators of multilinear singular integrals with generalized kernels

Liwen Gao, Yan Lin, Shuhui Yang

China University of Mining and Technology, Beijing; China University of Mining and Technology, Beijing; China University of Mining and Technology, Beijing

Abstract

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Abstract

In this paper, the weighted $L^{p}$ boundedness of multilinear commutators and multilinear iterated commutators generated by the multilinear singular integral operators with generalized kernels and BMO functions is established, where the weight is multiple weight. Our results are generalizations of the corresponding results for multilinear singular integral operators with standard kernels and Dini kernels under certain conditions.

Keywords: Multilinear singular integral with generalized kernel, multiple weights, iterated commutator, BMO function

MSC numbers: Primary 42B25, 42B35

Supported by: This work was financially supported by the National Natural Science Foundation of China (No. 12071052).