p-Adic Fractional Pseudodifferential Equations and Sobolev Type Spaces overp-Adic Fields

In this paper, we study the solutions of the pseudodifferential equations of type Dα u=v over p-adic field ℚp, where Dα is a p-adic fractional pseudodifferential operator. If v is a Bruhat-Schwartz function, then there exists a distribution Eα, a fundamental solution, such that u=Eα*v is a solution. We also show that the solution u belongs to a certain Sobolev space. Furthermore, we give conditions for the continuity and uniqueness of u