Embedding Theorems for Sobolev-Besicovitch Spaces of Almost Periodic Functions

Abstract

We show embedding theorems of Sobolev type for Sobolev-Besicovitch spaces $H^{m,q}_{ap}$ of almost periodic functions for any $q > 1$ and, consequently, for spaces $W^{m,q}_{ap}$, with $q \in (1, 2)$. The fundamental tool for the proof of the main theorem is the Hausdorff-Young theorem for almost periodic functions.