Approximation numbers of traces from anisotropic Besov spaces on anisotropic fractal $d$-sets

Preprint series: 06-04, Reports on Analysis

E. Tamási

The paper is published: Jenaer Schriften zur Mathematik und Informatik, Math/Inf/09/05, 2005; to appear in Rev. Mat. Complutense

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

Abstract: This paper deals with approximation numbers of the compact trace operator of an anisotropic Besov space into some $L_p$-space, $tr_\Gamma: B^{s,a}_{p,p}(\mathbb{R}^n) \rightarrow L_p(\Gamma), \quad s > 0, 1 < p < \infty,$
where $\Gamma$ is an anisotropic $d$-set, $0 < d < n$. We also prove homogeneity estimates, a homogeneous equivalent norm and the localisation property in $B^{s,a}_{p,p}(\mathbb{R}^n)$.

Keywords: anisotropic function spaces, fractals, wavelet frames