Limiting embeddings of Besov-type and Triebel-Lizorkin-type spaces on domains and an extension operator

In this paper, we study limiting embeddings of Besov-type and Triebel-Lizorkin-type spaces, id(tau) : B-p1,q1(s1,tau 1)(Omega) (sic) B-p2,q2(s2,tau 2)(Omega) and id(tau) : F-p1,q1(s1,tau 1)(Omega) (sic) F-p2,q2(s2,tau 2)(Omega), where Omega subset of R-d is a bounded domain, obtaining necessary and sufficient conditions for the continuity of id(tau). This can also be seen as the continuation of our previous studies of compactness of the embeddings in the non-limiting case. Moreover, we also construct Rychkov's linear, bounded universal extension operator for these spaces.