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.