**Preprint series:**
04-15, Analysis

**The paper is published:**
Jenaer Schriften zur Mathematik und Informatik, Math/Inf/06/04, 2004 /
J. Function Spaces Appl., 33-71, 3(1), 2005

**MSC:**- 46E35 Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
- 47B06 Riesz operators; eigenvalue distributions; approximation numbers, $s$-numbers, Kolmogorov numbers, entropy numbers, etc. of operators

**Abstract:** Continuity envelopes for the spaces of generalised smoothness $B^{(s,\Psi)}_{pq}(\rn)$ and $F^{(s,\Psi)}_{pq}(\rn)$ are studied in the so-called supercritical case $s=1+n/p$, paralleling recent developments for a corresponding limiting case for local growth envelopes of spaces of such a type. In addition, the power of the concept is used in proving conditions for some embeddings between function spaces to hold, as well as in the study of the asymptotic behaviour of approximation numbers of related embeddings.

**Keywords:** *Function spaces of generalised smoothness, continuity envelopes, sharp embeddings, approximation numbers*

**Upload:** 2004-03-29

**Update:** 2005
-11
-22

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