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

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.