Geodesic
Characterization of Lipschitz Functions via the Commutators of Maximal Functions on Stratified Lie Groups
Jianglong Wu1 ; Wenjiao Zhao2
1Department of Mathematics, Mudanjiang Normal University, P. R. China
2School of Mathematics, Physics and Finance, Anhui Polytechnic University, Wuhu, P. R. China
Journal of Lie Theory, Tome 33 (2023) no. 4, pp. 1177-1192

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 42B35, 43A80, 43A15
Mots-clés : Stratified Lie group, maximal function, Lipschitz function, commutator, Morrey space

Jianglong Wu  1   ; Wenjiao Zhao  2

1 Department of Mathematics, Mudanjiang Normal University, P. R. China
2 School of Mathematics, Physics and Finance, Anhui Polytechnic University, Wuhu, P. R. China 
Jianglong Wu; Wenjiao Zhao. Characterization of Lipschitz Functions via the Commutators of Maximal Functions on Stratified Lie Groups. Journal of Lie Theory, Tome 33 (2023) no. 4, pp. 1177-1192. http://geodesic.mathdoc.fr/item/JOLT_2023_33_4_a9/
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     author = {Jianglong Wu and Wenjiao 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},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2023_33_4_a9/}
}
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