Characterization of Lipschitz Space via the Commutators of Fractional Maximal Functions on Variable Lebesgue Spaces

2022/11/16 by Xuechun Yang, Yang, Xuechun, Zhenzhen Yang +3
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2211.08756

openalex publication_date 2022/11/16 · openalex created_date 2023/02/11 · openalex updated_date 2026/07/28

Abstract

We obtain some new characterizations of a variable version of Lipschitz spaces in terms of the boundedness of commutators of sharp maximal functions, fractional maximal functions or fractional maximal commutators in the context of the variable Lebesgue spaces, where the symbols of the commutators belong to the variable Lipschitz space. A useful tool is that a symbol b belongs a variable Lipschitz space of pointwise type if and only if b belongs to a variable Lipschitz space of integral type.

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