Besov Characteristic of a distribution

by    B. Vedel

Preprint series: 06-05, Reports on Analysis

B. Vedel

The paper is published: Jenaer Schriften zur Mathematik und Informatik, Math/Inf/10/05, 2005

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

Abstract: The Besov characteristic of a distribution $f$ is the function $s_f$ defined for $0\leq t < \infty$ by $s_f (t) = \sup\{s\in\mathbb{R}:f \in B^s_{1/t, 1}(\mathbb {R}^n)\}.$ We give in this paper a criterion for a function $\Gamma$ defined on $[0,\infty)$ to be the Besov characteristic of a distribution. Generalisations of this criterion to particular weighted Besov spaces and to anisotropic Besov spaces are also given.

Keywords: Besov spaces, wavelet analysis, weighted Besov spaces, anisotropic Besov spaces, anisotropic wavelets