Some extensions of the Marcinkiewicz interpolation theorem in terms of modular inequalities.
type: Item
instance of: scholarly article
title: Some extensions of the Marcinkiewicz interpolation theorem in terms of modular inequalities.
zbMATH Open document ID: 1042.46049
published in: Journal of the Mathematical Society of Japan
publication date: 2003-06-30T00:00:00Z
review text: Let \(({\mathcal M},\mu)\) and \(({\mathcal N},\nu)\) be two \(\sigma\)-finite measure spaces and let \(P\) and \(Q\) two modular functions (i.e., \(Q: [0,\infty)\to [0,\infty)\) is a nondecreasing right-continuous function with \(Q(0^+)= 0\)). For a given subadditive operator \(T: L^0(\mu)\to L^0(\nu)\), several mapping properties of interpolation type for which the modular inequality \[ \int_{\mathcal N} P(| Tf(x)|\,d\nu(x)\leq \int_{\mathcal M}Q(| f(x)|)\,d\mu(x) \] holds are studied and applied. These results generalize the classical Marcinkiewicz interpolation theorem.
reviewed by: Joaquim Martin
Mathematics Subject Classification ID: 46M35
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 1943316
zbMATH Keywords: boundedness of operators
zbMATH Keywords: interpolation
zbMATH Keywords: modular inequalities
author: María J. Carro
author: Ludmila Nikolova
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/1191419122
OpenAlex ID: W2077014204
DOI: 10.2969/JMSJ/1191419122
description: scientific article; zbMATH DE number 1943316