Beyond Besov spaces. II: Oscillation spaces
type: Item
instance of: scholarly article
title: Beyond Besov spaces. II: Oscillation spaces
zbMATH Open document ID: 1076.42024
author: Stéphane Jaffard
published in: Constructive Approximation
publication date: 2005-04-15T00:00:00Z
review text: In Part I of this work [J. Fourier Anal. Appl. 10, No.~3, 221--246 (2004; Zbl 1075.42014)], the author studied the information that for a function can be obtained from the distributions of wavelet coefficients at each scale. In this second part, new oscillation spaces are introduced through the distributions of suprema of wavelet coefficients on wavelet subtrees for functions that belong to the Besov spaces \(B^{s,\infty}_p\). These extensions of Besov spaces are sensitive to correlations between large wavelet coefficients located along lines of discontinuity and that are not revealed by Besov spaces. It is shown that these oscillation spaces do not depend on the particular wavelets selected and embedding properties between them and Besov spaces are described. Also, implications on dimensions of Hölder singularities, robustness properties and several examples taken from image processing and multifractal analysis are presented in this interesting paper.
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 26A16
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 94A08
zbMATH DE Number: 2157496
zbMATH Keywords: Besov spaces, Hausdorff dimension, oscillation spaces
zbMATH Keywords: wavelets
zbMATH Keywords: Hölder regularity
reviewed by: Joan Cerdà
MaRDI profile type: Publication
full work available at URL: s00365-004-0558-5
OpenAlex ID: W2000513984
DOI: 10.1007/S00365-004-0558-5
description: scientific article; zbMATH DE number 2157496