A weighted version of Journé's lemma
type: Item
instance of: scholarly article
title: A weighted version of Journé's lemma
zbMATH Open document ID: 0819.42009
DOI: 10.4171/RMI/155
author: Donald Krug
author: Alberto Torchinsky
published in: Revista Matemática Iberoamericana
publication date: 1995-07-25T00:00:00Z
full work available at URL: https://eudml.org/doc/39449
review text: The authors discuss a weighted version of Journé's covering lemma [see \textit{J. L. Journé}, Rev. Mat. Iberoam. 1, No. 3, 55-91 (1985; Zbl 0634.42015)]. The result is applied to obtain a sharp version of the atomic decomposition of the weighted Hardy spaces \(H_ w^ p (\mathbb{R}_ +^ 2\times \mathbb{R}_ +^ 2)\) and to describe the duals of these spaces for \(p\) close to 1 (specifically, in the latter case it is assumed that \(w\) satisfies the Muckenhoupt \(A_ r\)-condition on rectangles and that \(r/2< p\leq 1\)).
Mathematics Subject Classification ID: 42B30
Mathematics Subject Classification ID: 42B25
zbMATH DE Number: 647731
zbMATH Keywords: Muckenhoupt \(A_ p\)-condition on rectangles
zbMATH Keywords: Journé's covering lemma
zbMATH Keywords: weighted Hardy spaces
reviewed by: S. V. Kislyakov
MaRDI profile type: Publication
Wikidata QID: Q124800460
description: scientific article; zbMATH DE number 647731