Global orthogonality implies local almost-orthogonality
type: Item
instance of: scholarly article
title: Global orthogonality implies local almost-orthogonality
zbMATH Open document ID: 0967.42012
DOI: 10.4171/RMI/270
author: J. Michael Wilson
published in: Revista Matemática Iberoamericana
publication date: 2000-08-07T00:00:00Z
full work available at URL: https://eudml.org/doc/39590
review text: A family \(\{\phi_{(I)}: I\in{\mathcal D}\}\) of functions, where \({\mathcal D}\) denotes the usual family of dyadic cubes \(I\subset\mathbb{R}^d\), is said to be ``almost-orthogonal'' if for every finite-linear combination \[ f(x)= \sum_I\gamma_I \Phi_{(I)}(x), \] the inequality \[ \int|f|^2 dx\leq \sum_I |\gamma_I|^2 \] holds. Each function \(\phi_{(I)}\) is assumed to satisfy fairly weak decay, smoothness, and cancellation conditions. The author introduces a new stopping-time argument to prove a new Littlewood-Paley type result for such linear combinations \(f\), involving a weight function belonging to the class \(A_\infty\).
reviewed by: Ferenc Móricz
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 1485605
zbMATH Keywords: stopping-time
zbMATH Keywords: Littlewood-Paley type result
zbMATH Keywords: weight function
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1485605