Continuity of the maximal commutators in Sobolev spaces

Xixi Jiang; Feng Liu

doi:10.4134/JKMS.j230303

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(3): 461-494

Online first article February 26, 2024 Printed May 1, 2024

https://doi.org/10.4134/JKMS.j230303

Continuity of the maximal commutators in Sobolev spaces

Xixi Jiang, Feng Liu

Shandong University of Science and Technology; Shandong University of Science and Technology

Abstract

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Abstract

We prove the Sobolev continuity of maximal commutator and its fractional variant with Lipschitz symbols, both in the global and local cases. The main result in global case answers a question originally posed by Liu and Wang in \cite{LW}.

Keywords: Maximal commutator, fractional maximal commutator, Sobolev space, continuity

MSC numbers: Primary 42B20, 42B25

Supported by: The second author was supported partly by the Natural Science Foundation of Shandong Province (Grant no. ZR2023MA022) and the National Natural Science Foundation of China (Grant no. 12326371).