Characterization of Lipschitz Functions via the Commutators of Maximal Functions on Stratified Lie Groups

J. Wu; W. Zhao

doi:10.5802/jolt.1323

J. Wu; W. Zhao

Journal of Lie Theory, Volume 33 (2023) no. 4, pp. 1177-1192

Abstract

Our main aim is to consider the boundedness of the Hardy-Littlewood 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 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 M_b and [b, M] are given.

arXiv Zbl

DOI: 10.5802/jolt.1323

Classification: 42B35, 43A80, 43A15
Keywords: Stratified Lie group, maximal function, Lipschitz function, commutator, Morrey space

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     author = {J. Wu and W. Zhao},
     title = {Characterization of {Lipschitz} {Functions} via the {Commutators} of {Maximal} {Functions} on {Stratified} {Lie} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {1177--1192},
     year = {2023},
     volume = {33},
     number = {4},
     doi = {10.5802/jolt.1323},
     zbl = {1527.42034},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1323/}
}

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J. Wu; W. Zhao. Characterization of Lipschitz Functions via the Commutators of Maximal Functions on Stratified Lie Groups. Journal of Lie Theory, Volume 33 (2023) no. 4, pp. 1177-1192. doi: 10.5802/jolt.1323

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