Calderón-Zygmund operators on Morrey and Hardy-Morrey spaces in locally compact Vilenkin groups
type: Item
instance of: scholarly article
title: Calderón-Zygmund operators on Morrey and Hardy-Morrey spaces in locally compact Vilenkin groups
zbMATH Open document ID: 1489.43002
DOI: 10.1134/S2070046621030031
author: Kwok-Pun Ho
published in: \(p\)-Adic Numbers, Ultrametric Analysis, and Applications
publication date: 2021-12-27T00:00:00Z
review text: Let \(G\) be a locally compact Vilenkin group, \(p\in (0,\infty)\), \(\mathbb I\) be the collection of cosets in \(G\), and \(u : \mathbb I \rightarrow (0,\infty)\). The Morrey space \(\mathcal{M}_{p,u}(G)\) consists of all measurable functions \(f\) satisfying \[ \|f\|_{\mathcal{M}_{p,u}(G)}=\sup\limits_{I\in\mathbb I}\frac{1}{u(I)}\|\chi_I f\|_{L^p}<\infty. \] Conditions for a function \(u\) are obtained under which the Calderón-Zygmund operator is bounded in the Morrey space \(\mathcal{M}_{p,u}(G)\).
Mathematics Subject Classification ID: 43A15
Mathematics Subject Classification ID: 43A70
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 42C10
zbMATH DE Number: 7450874
zbMATH Keywords: Calderón-Zygmund operators
zbMATH Keywords: Hardy space
zbMATH Keywords: Morrey spaces
zbMATH Keywords: locally compact Vilenkin groups
zbMATH Keywords: local field
reviewed by: S. F. Lukomskii
MaRDI profile type: Publication
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full work available at URL: s2070046621030031
OpenAlex ID: W3198151328
description: scientific article; zbMATH DE number 7450874