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

Wu, Jianglong; Chang, Yunpeng

Comptes Rendus. Mathématique, Tome 362 (2024) no. G2, pp. 177-194

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 ${ℳ}_{\alpha }^p$ 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.

Classification : 42B35, 11E95, 26A16, 26A33, 47G10
Keywords: $p$-adic field, Lipschitz function, fractional maximal function, variable exponent Lebesgue space

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