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

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 α 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.