by **
D. Haroske**

**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*

**Upload:** 1999-01-28

**Update:** 1999-01-28

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