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

Abstract EN

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.