Commutators of the maximal and sharp functions with weighted Lipschitz functions

2023/07/28 by Zhang, Pu, Zhu, Xiaomeng
#26A16 #42B20 #42B25 #47B47 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2307.15500

Abstract

Let M be the Hardy-Littlewood maximal function. Denote by M_b and [b,M] the maximal and the nonlinear commutators of M with a function b. The boundedness of M_b and [b,M] on weighted Lebesgue spaces are characterized when the symbols b belong to weighted Lipschitz (weighted Morrey-Campanato) spaces. Some new characterizations for weighted Lipschitz spaces are obtained. Similar results are also established for the nonlinear commutator of the sharp function.

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