Optimal Calderón Spaces for generalized Bessel potentials

Abstract

In the paper we investigate the properties of spaces with generalized smoothness, such as Calderón spaces that include the classical Nikolskii-Besov spaces and many of their generalizations, and describe differential properties of generalized Bessel potentials that include classical Bessel potentials and Sobolev spaces. Kernels of potentials may have non-power singularity at the origin. With the help of order-sharp estimates for moduli of continuity of potentials, we establish the criteria of embeddings of potentials into Calderón spaces, and describe the optimal spaces for such embeddings.