Multiresolution approximations and wavelet bases of weighted \(L^p\) spaces
type: Item
instance of: scholarly article
title: Multiresolution approximations and wavelet bases of weighted \(L^p\) spaces
zbMATH Open document ID: 1067.42019
author: Hugo Aimar
author: A. L. Bernardis
author: F. J. Martín-Reyes
published in: The Journal of Fourier Analysis and Applications
publication date: 2004-09-22T00:00:00Z
review text: In this paper necessary and sufficient conditions on the Borel measure \( \mu \) of \(\mathbb R^n\) are obtained for which there is a mean and almost everywhere convergence of multiresolution approximations of \( L^p(d\mu ) \) functions if the scaling function is assumed to be continuous and absolutely bounded by an \( L^1 \) radial decreasing function. The approach relies on a weak positivity property of the kernels of the projection operators. Further, necessary and sufficient conditions on the Borel measure \( \mu \) for the associated wavelet systems to be unconditional bases for the space \( L^p(d\mu ) \) are studied.
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 42B20
zbMATH DE Number: 2102103
zbMATH Keywords: wavelets
zbMATH Keywords: weighted Lebesgue spaces, unconditional basis
zbMATH Keywords: projection operators
zbMATH Keywords: \(A_p\) weights
reviewed by: Gerlind Plonka
MaRDI profile type: Publication
full work available at URL: s00041-003-0024-y
OpenAlex ID: W2162805190
DOI: 10.1007/S00041-003-0024-Y
description: scientific article; zbMATH DE number 2102103