Journal of Lie Theory 33 (2023), No. 4, 1177--1192
Copyright Heldermann Verlag 2023
Characterization of Lipschitz Functions via the Commutators of Maximal Functions on Stratified Lie Groups
Jianglong Wu
Department of Mathematics, Mudanjiang Normal University, P. R. China
jl-wu@163.com
Wenjiao Zhao
School of Mathematics, Physics and Finance, Anhui Polytechnic University, Wuhu, P. R. China
zhaowenjiao@mail.ahpu.edu.cn
Our main aim is to consider the boundedness of the Hardy-Littlewood maximal commutator Mb and the nonlinear commutator [b, M] on the Lebesgue spaces and Morrey spaces over some stratified Lie group G when the symbols of the commutators belong to the Lipschitz space. Meanwhile, the corresponding end-point estimates on the Lebesgue spaces and Morrey spaces over some stratified Lie group G are considered as well. As a result, some new characterizations of the Lipschitz spaces on Lie group via Mb and [b, M] are given.
Keywords: Stratified Lie group, maximal function, Lipschitz function, commutator, Morrey space.
MSC: 42B35, 43A80, 43A15.
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