Compact embeddings in Besov-type and Triebel-Lizorkin-type Spaces on bounded domains

Abstract

We study embeddings of Besov-type and Triebel-Lizorkin-type spaces, idτ : B s 1 ,τ 1 p 1 ,q 1 (Ω) ֒→ B s 2 ,τ 2 p 2 ,q 2 (Ω) and idτ :where Ω ⊂ R d is a bounded domain, and obtain necessary and sufficient conditions for the compactness of idτ . Moreover, we characterise its entropy and approximation numbers. Surprisingly, these results are completely obtained via embeddings and the application of the corresponding results for classical Besov and Triebel-Lizorkin spaces as well as for Besov-Morrey and Triebel-Lizorkin-Morrey spaces.

Triebel–Lizorkin–Morrey spaces and differences

“…Proof. Situation (i) can be found in [6], see Corollary 3.10. Let us look at the cases (ii) and (iii).…”