The molecular characterization of weighted Hardy spaces
type: Item
instance of: scholarly article
title: The molecular characterization of weighted Hardy spaces
zbMATH Open document ID: 0998.42013
author: Ming-Yi Lee
author: Chin-Cheng Lin
published in: Journal of Functional Analysis
publication date: 2002-07-04T00:00:00Z
review text: Let \(0<p\leq 1\leq q\leq\infty\), \(p\neq q\) and \(\omega\in A_q\) (the Muckenhoupt's class). The authors introduce the weighted molecules which characterize the weighted Hardy spaces \(H^p_\omega(\mathbb R^n)\). As an application, the authors give some sufficient conditions on the kernel \(k\) such that the convolution operator \(Tf=k\ast f\) is bounded on weighted Hardy spaces \(H^p_\omega(\mathbb R^n)\) for some \(p\leq 1\) and \(\omega\in A_1\). The authors also prove that the Hilbert transform is bounded on \(H^p_\omega(\mathbb R)\) for \(1/2<p\leq 1\) and \(\omega\in A_1\) and that the Riesz transforms are bounded on \(H^p_\omega(\mathbb R^n)\) for \(n/(n+1)<p\leq 1\) and \(\omega\in A_1\).
Mathematics Subject Classification ID: 42B30
Mathematics Subject Classification ID: 42B20
zbMATH DE Number: 1763778
zbMATH Keywords: weight
zbMATH Keywords: atom
zbMATH Keywords: molecule
zbMATH Keywords: Hilbert transform
zbMATH Keywords: Riesz transform
zbMATH Keywords: singular integral
zbMATH Keywords: weighted Hardy space
reviewed by: Dachun Yang
MaRDI profile type: Publication
full work available at URL: jfan.2001.3839
OpenAlex ID: W2009614184
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DOI: 10.1006/JFAN.2001.3839
description: scientific article; zbMATH DE number 1763778