Integral convolution operators
type: Item
instance of: scholarly article
title: Integral convolution operators
zbMATH Open document ID: 0659.46034
DOI: 10.1007/BF01137467
author: E. A. Pavlov
published in: Mathematical Notes
publication date: 1985-01-01T00:00:00Z
review text: Let \(E_ 1,E_ 2\) and \(E_ 3\) be symmetric function spaces on an interval [0,a]. The following problem is under investigation: under which conditions is the convolution operator continuous from \(E_ 1\times E_ 2\) into \(E_ 3?\) The author gives some sufficient conditions for the continuity in terms of the Boyd indices \(\alpha_ E\) and \(\beta_ E\) of a space E. For example, if \(\beta_{E_ 3}+\beta_{E_ 1}<1+\alpha_{E_ 2}\) and \(\alpha_{E_ 1}+\beta_{E_ 3}>1\), then the convolution operator maps \(E_ 1\times E_ 2\) continuously into \(E_ 3\).
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 47Gxx
Mathematics Subject Classification ID: 44A35
zbMATH DE Number: 4078016
zbMATH Keywords: symmetric function spaces on an interval
zbMATH Keywords: convolution operator
zbMATH Keywords: sufficient conditions for the continuity in terms of the Boyd indices
MaRDI profile type: Publication
cites work: Q4097705
cites work: Convolution operators and L(p, q) spaces
cites work: Q3961369
description: scientific article; zbMATH DE number 4078016