
Journal of Lie Theory 33 (2023), No. 4, 11771192 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 jlwu@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 HardyLittlewood maximal commutator M_{b} 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 endpoint 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 M_{b} and [b, M] are given. Keywords: Stratified Lie group, maximal function, Lipschitz function, commutator, Morrey space. MSC: 42B35, 43A80, 43A15. [ Fulltextpdf (150 KB)] for subscribers only. 