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.

In this paper, we establish the sharp constant for q -analogus of Hausdorff operators on central q -Morrey spaces. As applications, the sharp constants for the q -analogus of Hardy operator and its dual operator, the q -analogue of Hardy-Littlewood-Pólya operator, and the q -analogue of Hilbert operator on central q -Morrey spaces are deduced.