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Theory Article | Open Access

Boundedness and continuity of local bilinear maximal commutators on Triebel–Lizorkin spaces and Besov spaces

Feng Liu1, Simin Liu1, Xiao Zhang2( )
College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao, Shandong Province 266590, China
College of Electronic and Information Engineering, Shandong University of Science and Technology, Qingdao, Shandong Province 266590, China
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Abstract

In the present paper we investigated the mapping properties for the bilinear maximal commutator in the domain setting. Some new boundedness and continuity for the above operator on the Triebel–Lizorkin spaces and Besov spaces were established under suitable symbol function conditions. The main results essentially extend some known ones to the local setting.

Keywords

local bilinear maximal commutatorTriebel–Lizorkin spaceBesov spaceboundedness and continuity
CLC number: 42B25, 46E35

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AIMS Mathematics
Volume 11 Issue 1,
January 2026
Pages 167-191
DOI: 10.3934/math.2026007

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Cite this article:
Liu F, Liu S, Zhang X. Boundedness and continuity of local bilinear maximal commutators on Triebel–Lizorkin spaces and Besov spaces. AIMS Mathematics, 2026, 11(1): 167-191. https://doi.org/10.3934/math.2026007

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Received: 11 November 2025
Revised: 08 December 2025
Accepted: 18 December 2025
Published: 04 January 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)