**Preprint series:**
05-17, Analysis

**The paper is published:**
Jenaer Schriften zur Mathematik und Informatik, Math/Inf/06/05, 2005

**MSC:**- 46E35 Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
- 42B25 Maximal functions, Littlewood-Paley theory
- 28A80 Fractals [See also 37Fxx]

**Abstract:** This paper deals with atomic decompositions in spaces of type $B^s_{p,q}(\rn, w)$, $F^s_{p,q}\rn, w)$, $0<p<\infty$, $0<q\leq\infty$, $s\in\real$, where the weight function $w $ belongs to some Muckenhoupt class $\mathcal{A}_r$. In particular, we consider the weight function $w_\varkappa (x) = \dist(x,\Gamma)^\varkappa$, where $\Gamma$ is some $d$-set, $0<d<n$, and $\varkappa > -(n-d)$.

**Keywords:** *weighted function spaces, atomic decomposition, Muckenhoupt weights, $d$-sets*

**Upload:** 2005-06-15

**Update:** 2005
-11
-22

The author(s) agree, that this abstract may be stored as full text and distributed as such by abstracting services.