Wavelet frames in anisotropic Besov spaces

Preprint series: 05-16, Analysis

The paper is published: Jenaer Schriften zur Mathematik und Informatik, Math/Inf/01/05, 2005 / Georgian Math. J., to appear

MSC:
46E35 Sobolev spaces and other spaces of smooth'' functions, embedding theorems, trace theorems
42C40 Wavelets
42B35 Function spaces arising in harmonic analysis

Abstract: This paper deals with wavelet frames in anisotropic Besov spaces $B_{pq}^{s,a}(\rn)$, $s\in\real$, $0<p,q\leq\infty$, and $a=(a_1,\dots,a_n)$ an anisotropy, $a_i>0$, $a_1+ \cdots + a_n=n$. We present sub-atomic and wavelet decompositions
for a large class of distributions. To some extent our results can be regarded as anisotropic counterparts of those recently obtained in [34].

Keywords: anisotropic function spaces, sub-atomic decomposition, wavelet decomposition, wavelet frames