Atomic decomposition characterizations of weighted multiparameter Hardy spaces
type: Item
instance of: scholarly article
title: Atomic decomposition characterizations of weighted multiparameter Hardy spaces
zbMATH Open document ID: 1278.42028
author: Xinfeng Wu
published in: Frontiers of Mathematics in China
publication date: 2013-04-10T00:00:00Z
review text: Let \(\omega\in A_{\infty}(\mathbb{R}^n \times \mathbb{R}^m)=\bigcup_{1\leq q<\infty}A_q\). Let \(q_{\omega}=\inf\{q: \omega\in A_q\}\) be the critical index of \(\omega\). The author introduces the weighted-\((p, q)\) atomic Hardy spaces \( H^{p,q}_\omega (\mathbb{R}^n \times \mathbb{R}^m)\) for \(0 < p\leq 1\), \(q >q_{\omega}\) and shows that the weighted Hardy space \( H^{p}_\omega (\mathbb{R}^n \times \mathbb{R}^m)\) defined via Littlewood-Paley square functions coincides with \( H^{p,q}_\omega (\mathbb{R}^n \times \mathbb{R}^m)\) for \(0 < p\leq 1\), \(q >q_{\omega}\). As applications, the author proves that a linear operator \(T\) is bounded from \( H^{p}_\omega (\mathbb{R}^n \times \mathbb{R}^m)\) to \( L^{p}_\omega (\mathbb{R}^n \times \mathbb{R}^m)\), when \(T\) is bounded on \( H^{p}_\omega (\mathbb{R}^n \times \mathbb{R}^m)\) and on \( L^{q}_\omega (\mathbb{R}^n \times \mathbb{R}^m)\) for \(q >q_{\omega}\) and obtains a boundedness criterion for two parameter singular integrals on weighted Hardy spaces.
reviewed by: Yu Liu
Mathematics Subject Classification ID: 42B30
Mathematics Subject Classification ID: 42B25
zbMATH DE Number: 6152751
zbMATH Keywords: atomic decomposition
zbMATH Keywords: multiparameter Hardy space
zbMATH Keywords: \(A_{\infty}\) weight
MaRDI profile type: Publication
full work available at URL: s11464-012-0213-6
OpenAlex ID: W1989539945
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DOI: 10.1007/S11464-012-0213-6
description: scientific article; zbMATH DE number 6152751