Compact embeddings of Sobolev, Besov, and Triebel-Lizorkin spaces
Compact embeddings of Sobolev, Besov, and Triebel-Lizorkin spaces
We establish necessary and sufficient conditions guaranteeing compactness of embeddings of fractional Sobolev spaces, Besov spaces, and Triebel-Lizorkin spaces, in the general context of quasi-metric-measure spaces. Although stated in the setting of quasi-metric spaces, the main results in this article are new, even in the metric setting. Moreover, by considering …