Stability of wavelet-like expansions under chromatic aberration
type: Item
instance of: scholarly article
title: Stability of wavelet-like expansions under chromatic aberration
zbMATH Open document ID: 1170.42017
published in: Journal of Mathematical Analysis and Applications
publication date: 2009-04-29T00:00:00Z
review text: Let \({\mathcal D}\) denote the collection of dyadic cubes in \(\mathbb{R}^d\), let \({\mathcal F}\) be a finite subset of \({\mathcal D}\), and let \(\{\phi^{(Q)}\}_{Q \in {\mathcal D}}\) and \(\{\psi^{(Q)}\}_{Q \in {\mathcal D}}\) be two families of functions, both indexed in \(\mathbb{R}^d\), that satisfy certain uniform decay, cancellation and smoothness conditions that make them ``wavelet--like''. Given a function \(h\), the author defines a certain normalized translation operator \(h_Q\) and, for weights \(w\) in the Muckenhoupt class \(A_p\), studies the \(L^p(w)\) stability of operators of the form \[ T(f) := \sum_{Q \in {\mathcal F}} \langle f, \phi^Q_Q \rangle \psi^Q_Q \] under small perturbations in the arguments of the functions \(\phi^Q\) and \(\psi^Q\).
reviewed by: Richard A. Zalik
Mathematics Subject Classification ID: 42C15
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 5549415
zbMATH Keywords: Littlewood--Paley Theory
zbMATH Keywords: Muckenhoupt class
zbMATH Keywords: weighted norm inequality
zbMATH Keywords: wavelet
zbMATH Keywords: perturbation
zbMATH Keywords: stability
author: J. Michael Wilson
MaRDI profile type: Publication
full work available at URL: j.jmaa.2008.11.053
OpenAlex ID: W2086738658
cites work: Q4526789
cites work: Q3922907
cites work: Q3700300
cites work: Q3142876
DOI: 10.1016/J.JMAA.2008.11.053
description: scientific article; zbMATH DE number 5549415