Characterization of Lipschitz spaces via commutators of the Hardy–Littlewood maximal function

Pu Zhang

doi:10.1016/j.crma.2017.01.022

Harmonic analysis

Characterization of Lipschitz spaces via commutators of the Hardy–Littlewood maximal function

the Editorial Board

Pu Zhang ¹

¹Department of Mathematics, Mudanjiang Normal University, Mudanjiang 157011, PR China

Comptes Rendus. Mathématique, Volume 355 (2017) no. 3, pp. 336-344

Abstract (Original language)
Résumé

Let M be the Hardy–Littlewood maximal function and b be a locally integrable function. Denote by $M_{b}$ and $[b, M]$ the maximal commutator and the (nonlinear) commutator of M with b. In this paper, the author considers the boundedness of $M_{b}$ and $[b, M]$ on Lebesgue spaces and Morrey spaces when b belongs to the Lipschitz space, by which some new characterizations of the Lipschitz spaces are given.

Soit M l'opérateur maximal de Hardy–Littlewood et b une fonction localement intégrable. Notons $M_{b}$ et $[b, M]$ le commutateur maximal et le commutateur (non linéaire) de M et b. Dans cette Note, l'auteur étudie la finitude de $M_{b}$ et $[b, M]$ sur les espaces de Lebesgue et les espaces de Morrey lorsque b appartient à l'espace de Lipschitz. Cela conduit à de nouvelles caractérisations de l'espace de Lipschitz.

Article information
Cite this article

Received: 2016-11-06
Accepted: 2017-02-01
Published online: 2017-02-20

DOI: 10.1016/j.crma.2017.01.022

Author's affiliations:

Pu Zhang ¹

¹ Department of Mathematics, Mudanjiang Normal University, Mudanjiang 157011, PR China

Pu Zhang. Characterization of Lipschitz spaces via commutators of the Hardy–Littlewood maximal function. Comptes Rendus. Mathématique, Volume 355 (2017) no. 3, pp. 336-344. doi: 10.1016/j.crma.2017.01.022

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     doi = {10.1016/j.crma.2017.01.022},
     language = {en},
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^☆ Supported by the National Natural Science Foundation of China (Grant Nos. 11571160 and 11471176).

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