Some limiting embeddings in weighted function spaces and related entropy numbers.

Preprint series: 97-01, Analysis

The paper is published: Forschungsergebnisse, Math/Inf/97/04, Universität Jena, Germany, 1997

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

Abstract: The paper deals with weighted function spaces of type $B^s_{p,q}({\Bbb{R}}^n,w(x))$ and
$F^s_{p,q}({\Bbb{R}}^n,w(x))$, where $w(x)$ is a weight function of at most polynomial growth. Of special
interest are weight functions of type $w(x)=(1+|x|^2)^{\alpha/2}\,(\log(2+|x|))^\mu\;$ with $\alpha\geq 0$ and $\mu\in {\Bbb{R}}$.
Our main result deals with estimates for the entropy numbers of compact embeddings between
spaces of this type; more precisely, we may extend and tighten some of our previous results.

Keywords: weighted function spaces, compact embeddings, entropy numbers