Convolution operators on Banach-Orlicz algebra
type: Item
instance of: scholarly article
title: Convolution operators on Banach-Orlicz algebra
zbMATH Open document ID: 1463.47116
author: Ali Ebadian
author: Ali Jabbari
published in: Analysis Mathematica
publication date: 2020-10-02T00:00:00Z
review text: For a locally compact group \(G\), let \(\mathcal{L}^{\Phi} (G)\) and \(\mathcal{L}_{\omega}^{\Phi} (G)\) denote the Orlicz and weighted Orlicz spaces, respectively, where \(\Phi\) is a Young function and \(\omega\) is a weight on \(G\). The authors study harmonic and convolution operators on Orlicz and weighted Orlicz spaces. In Section 4, they consider the harmonic operators on \(\mathcal{L}^{\Phi} (G)\) and study their compactness. In Proposition 4.4, they prove that, for a compact group \(G\) with normalized Haar measure \(\lambda\), and \(\mu\in M(G)\) and \(\Phi\in \Delta'\) satisfying a certain extra hypotheses, then a harmonic operator \(T_{\mu}\) on \(\mathcal{L}^{\Phi} (G)\) is weakly compact if and only if it is compact if and only if \(\mu\) is absolutely continuous. Compact harmonic operators on \(\mathcal{L}_{\omega}^{\Phi} (G)\) are characterized in Theorem 4.14. The last section is devoted to characterizing the convolution operators on Orlicz and weighted Orlicz spaces.
reviewed by: Antonio M. Peralta
Mathematics Subject Classification ID: 47B48
Mathematics Subject Classification ID: 46E25
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 7254982
zbMATH Keywords: convolution operator
zbMATH Keywords: harmonic operator
zbMATH Keywords: locally compact group
zbMATH Keywords: Orlicz space
zbMATH Keywords: weighted Orlicz space
MaRDI profile type: Publication
full work available at URL: s10476-020-0023-0
OpenAlex ID: W3014751264
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DOI: 10.1007/S10476-020-0023-0
description: scientific article; zbMATH DE number 7254982