Convolution operators on the weighted Herz-type Hardy spaces
type: Item
instance of: scholarly article
title: Convolution operators on the weighted Herz-type Hardy spaces
zbMATH Open document ID: 1087.42011
author: Ming-Yi Lee
published in: Journal of Approximation Theory
publication date: 2006-03-20T00:00:00Z
review text: Let \(0<p\leq 1 <q<\infty\) and \(w \in A_1\) (the weight class of Muckenhoupt). In this paper, the author first establishes a weighted molecular characterization for the weighted Herz-type Hardy spaces \(H\dot{K}_q^{n(1/p-1/q),p}(w,w)\) and \(HK_q^{n(1/p-1/q),p}(w,w)\). Using this characterization, the author then obtains the boundedness of the convolution operator \(Tf=k*f\) in the weighted Herz-type Hardy spaces when \(p\leq 1\). In particular, the boundedness of the Hilbert transform and the Riesz transforms in these weighted Herz-type Hardy spaces when \(0<p\leq 1\) can be deduced from these results.
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 42B30
zbMATH DE Number: 5013602
zbMATH Keywords: central atom
zbMATH Keywords: molecule
zbMATH Keywords: Hardy space
zbMATH Keywords: Herz space
zbMATH Keywords: weight
zbMATH Keywords: boundedness
reviewed by: Dachun Yang
MaRDI profile type: Publication
full work available at URL: j.jat.2005.11.007
OpenAlex ID: W2088401945
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DOI: 10.1016/J.JAT.2005.11.007
description: scientific article; zbMATH DE number 5013602