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

Feng Liu; Simin Liu; Xiao Zhang; Feng Liu; Simin Liu; Xiao Zhang

doi:10.3934/math.2026007

AIMS Mathematics

2026, Volume 11, Issue 1: 167-191. doi: 10.3934/math.2026007

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

1.
College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao, Shandong Province 266590, China
2.
College of Electronic and Information Engineering, Shandong University of Science and Technology, Qingdao, Shandong Province 266590, China

Received: 11 November 2025 Revised: 08 December 2025 Accepted: 18 December 2025 Published: 04 January 2026
MSC : 42B25, 46E35

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.
- local bilinear maximal commutator,
- Triebel–Lizorkin space,
- Besov space,
- boundedness and continuity
Citation: Feng Liu, Simin Liu, Xiao Zhang. Boundedness and continuity of local bilinear maximal commutators on Triebel–Lizorkin spaces and Besov spaces[J]. AIMS Mathematics, 2026, 11(1): 167-191. doi: 10.3934/math.2026007

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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.

References

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