Quantifying democracy of wavelet bases in Lorentz spaces
type: Item
instance of: scholarly article
title: Quantifying democracy of wavelet bases in Lorentz spaces
zbMATH Open document ID: 1223.41007
author: E. Hernández
author: Maria de Natividade
author: José María Martell
published in: Constructive Approximation
publication date: 2011-02-14T00:00:00Z
review text: The \(h_l\) and \(h_r\), democracy functions of admissible wavelet bases for Lorentz spaces \(L^{p,q}(\mathbb R^d)\), \(1<p<\infty\), \(1\leq q < \infty\) are computed in this paper. The authors show that \[ h_l(N)=N^{1/\max{p,q}}, \qquad h_l(N)=N^{1/\min{p,q}}. \] This result is used to give sharp inclusions for the approximation spaces in terms of discrete Lorentz sequence spaces.
Mathematics Subject Classification ID: 41A17
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 5851419
zbMATH Keywords: greedy algorithm
zbMATH Keywords: nonlinear approximation
zbMATH Keywords: Lorentz spaces
zbMATH Keywords: wavelets
zbMATH Keywords: approximation spaces
reviewed by: Joaquim Martin
MaRDI profile type: Publication
full work available at URL: s00365-010-9113-8
OpenAlex ID: W2052904200
cites work: Restricted nonlinear approximation
cites work: Q3797727
cites work: The thresholding greedy algorithm, greedy bases, and duality
cites work: Sharp Jackson and Bernstein inequalities for N-term approximation in sequence spaces with applications
cites work: Wavelets, Orlicz spaces, and greedy bases
cites work: Q4896587
cites work: Q4365119
cites work: Greedy approximation and the multivariate Haar system
cites work: Nonlinear approximation and Muckenhoupt weights
cites work: A remark on greedy approximation in Banach spaces.
cites work: Unconditional biorthogonal wavelet bases in~\(L^p ({\mathbb R}^d)\)
cites work: Wavelet bases in rearrangement invariant function spaces
cites work: Q5640160
cites work: The best \(m\)-term approximation and greedy algorithms
cites work: Wavelets as unconditional bases in \(L_p(\mathbb{R})\)
cites work: Q3414502
DOI: 10.1007/S00365-010-9113-8
description: scientific article; zbMATH DE number 5851419