Embedding Theorems for Sobolev-Besicovitch Spaces of Almost Periodic Functions

Abstract

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