Compactness of Sobolev embeddings and decay of norms

Abstract

We investigate the relationship between the compactness of embeddings of Sobolev spaces built upon rearrangement-invariant spaces into rearrangement-invariant spaces endowed with d-Ahlfors measures under certain restriction on the speed of their decay on balls.

Keywords

• Compactness
• Sobolev
• embeddings
• decay