Equivalence of Haar bases associated with different dyadic systems
type: Item
instance of: scholarly article
title: Equivalence of Haar bases associated with different dyadic systems
zbMATH Open document ID: 1219.42019
author: Hugo Aimar
author: Luis Nowak
author: A. L. Bernardis
published in: The Journal of Geometric Analysis
publication date: 2011-05-13T00:00:00Z
full work available at URL: http://cimec.org.ar/ojs/index.php/cmm/article/view/2962
review text: The authors consider a general notion of equivalence for dyadic systems on a metric space of homogeneous type that originate equivalent Haar systems for weighted Lebesgue spaces. The main reference is [\textit{M. Christ}, Colloq. Math. 60/61 (2), 601--628 (1990; Zbl 0758.42009)] and, as an application of their results, it is shown that Haar bases built on dyadic families of M. Christ with the same basic nets of points but different orders are equivalent. Basic tools are the vector-valued maximal Fefferman-Stein inequality on Lebesgue spaces with Muckenhoupt weights, and the characterization of weighted Lebesgue spaces via Haar coefficients.
Mathematics Subject Classification ID: 42C15
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 28C15
zbMATH DE Number: 5887815
zbMATH Keywords: Haar basis
zbMATH Keywords: equivalence of bases
zbMATH Keywords: spaces of homogeneous type
zbMATH Keywords: Muckenhoupt weights
reviewed by: Joan Cerdà
MaRDI profile type: Publication
OpenAlex ID: W2086996211
cites work: Multiresolution approximations and unconditional bases on weighted Lebesgue spaces on spaces of homogeneous type
cites work: A T(b) theorem with remarks on analytic capacity and the Cauchy integral
cites work: Q2548398
cites work: Some Maximal Inequalities
cites work: Q4238947
cites work: A new class of unbalanced Haar wavelets that form an unconditional basis for \(L_ p\) on general measure spaces
cites work: Q4896587
cites work: A remark on greedy approximation in Banach spaces.
cites work: A decomposition into atoms of distributions on spaces of homogeneous type
cites work: Square integrable martingales orthogonal to every stochastic integral
cites work: Q3955832
DOI: 10.1007/S12220-010-9148-X
description: scientific article; zbMATH DE number 5887815