Atomic decompositions of function spaces with Muckenhoupt weights; an example from fractal geometry

by    D.D. Haroske, I. Piotrowska

Preprint series: 05-17, Analysis

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

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

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