Continuous and compact embeddings of Bessel-potential-type spaces

Abstract

We survey, comment and complement our results on embeddings of Bessel potential spaces modelled upon Lorentz-Karamata spaces. Target spaces in our embeddings are either Lorentz-Karamata spaces or generalized H\"older spaces.

In particular, we establish necessary and sufficient conditions both for continuous and compact embeddings of spaces in question.

Keywords

• Continuous embeddings
• compact embeddings
• Bessel-potential-type spaces
• Lorentz-Karamata spaces
• generalized H\"older spaces