Compact Embeddings of Bessel-Potential-Type Spaces into Generalized Hoelder Spaces Involving k-Modulus of Smoothness

Abstract

We present conditions which are necessary and sufficient for compact embeddings of Bessel potential spaces, modelled upon a rearrangement- -invariant Banach function spaces, into generalized Hoelder spaces involving k-modulus of smoothness.

Keywords

• Bessel potentials
• (fractional) Sobolev-type spaces
• rearrangement-invariant Banach function spaces
• generalized Hoelder-type spaces
• embedding theorems