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Zeitschrift für Analysis und ihre Anwendungen


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Volume 17, Issue 2, 1998, pp. 443–457
DOI: 10.4171/ZAA/832

Published online: 1998-06-30

Embedding Theorems for Sobolev-Besicovitch Spaces of Almost Periodic Functions

R. Iannacci[1], A.M. Bersani[2], G. Dell'Acqua[3] and P. Santucci[4]

(1) Università di Roma La Sapienza, Italy
(2) Università di Roma La Sapienza, Italy
(3) Università di Roma La Sapienza, Italy
(4) Università di Roma La Sapienza, Italy

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.

Keywords: Almost periodic functions, embedding theorems, Sobolev-Besicovitch spaces

Iannacci R., Bersani A.M., Dell'Acqua G., Santucci P.: Embedding Theorems for Sobolev-Besicovitch Spaces of Almost Periodic Functions. Z. Anal. Anwend. 17 (1998), 443-457. doi: 10.4171/ZAA/832