Characterization of Lipschitz Spaces via Commutators of Maximal Function on the p -Adic Vector Space

Abstract

In this paper, we give characterization of a $p$ -adic version of Lipschitz spaces in terms of the boundedness of commutators of maximal function in the context of the $p$ -adic version of Lebesgue spaces and Morrey spaces, where the symbols of the commutators belong to the Lipschitz spaces. A useful tool is a Lipschitz norm involving the John-Nirenberg-type inequality for homogeneous Lipschitz functions, which is new in the $p$ -adic field context.