Characterization of Lipschitz Spaces via Commutators of Fractional Maximal Function on the $p$-Adic Variable Exponent Lebesgue Spaces

J. Wu; Y. Chang

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arXiv · 2306.10470

Characterization of Lipschitz Spaces via Commutators of Fractional Maximal Function on the $p$-Adic Variable Exponent Lebesgue Spaces

J. Wu·Y. Chang

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Abstract

In this paper, the main aim is to give some characterizations of the boundedness of the maximal or nonlinear commutator of the $p$-adic fractional maximal operator $ \mathcal{M}_{\alpha}^{p}$ with the symbols belong to the $p$-adic Lipschitz spaces in the context of the $p$-adic version of variable Lebesgue spaces, by which some new characterizations of the Lipschitz spaces and nonnegative Lipschitz functions are obtained in the $p$-adic field context. Meanwhile, Some equivalent relations between the $p$-adic Lipschitz norm and the $p$-adic variable Lebesgue norm are also given.

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BibTeX RIS

J. Wu, Y. Chang. 2023-06-18. Characterization of Lipschitz Spaces via Commutators of Fractional Maximal Function on the $p$-Adic Variable Exponent Lebesgue Spaces. https://arxiv.org/abs/2306.10470

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