Pseudo-differential Operators with Semi-Quasielliptic Symbols Over p-adic Fields

Abstract

In this article, we study pseudo-differential equations involving semi-quasielliptic symbols over p-adics. We determine the function spaces where such equations have solutions. We introduce the space of infinitely pseudo-differentiable functions with respect to a semi-quasielliptic operator. By using these spaces we show the existence of a regularization effect for certain parabolic equations over p-adics.Comment: Accepted in Journal of Mathemaatical Analysis and its Application