Continuity envelopes and sharp embeddings in spaces of generalized smoothness

Preprint series: 06-14, Analysis

The paper is published: Jenaer Schriften zur Mathematik und Informatik, Math/Inf/19/06, 2006

MSC:
46E35 Sobolev spaces and other spaces of smooth'' functions, embedding theorems, trace theorems

Abstract: We study continuity envelopes in spaces of generalized smoothness $B^{\sigma,N}_{p,q}(\mathbb{R}^n)$ and $F^{\sigma,N}_{p,q}(\mathbb{R}^n)$.
The results are applied in proving sharp embedding assertions in some limiting situations.

Keywords: spaces of generalized smoothness, limiting embeddings, continuity envelopes