Inequalites and properties of some generalized Orlicz classes and spaces
type: Item
instance of: scholarly article
title: Inequalites and properties of some generalized Orlicz classes and spaces
zbMATH Open document ID: 1164.26016
author: Lars-Erik Persson
author: Priti Upreti
author: Pankaj Jain
published in: Acta Mathematica Hungarica
publication date: 2008-11-19T00:00:00Z
review text: The generalized Orlicz classes \(\widetilde{X}_{\Phi}\) and generalized Orlicz spaces \(X_{\Phi}\) are defined by replacing the space \(L^{1}\) in the classical construction of Orlicz classes \(\widetilde{L}_{\Phi }\) and Orlicz spaces \(L_{\Phi }\) by an arbitrary Banach function space \(X.\) The authors prove some results which are important for the study of inequalities in these spaces. In particular, they prove some natural generalizations of the classical Minkowski's inequality, Hölder's inequality and Young's inequality.
reviewed by: Gheorghe Toader
Mathematics Subject Classification ID: 26D10
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 5368583
zbMATH Keywords: inequalites
zbMATH Keywords: function spaces
zbMATH Keywords: Orlicz class
zbMATH Keywords: Orlicz space
zbMATH Keywords: Luxemburg norm
zbMATH Keywords: Banach function space
zbMATH Keywords: Young function
zbMATH Keywords: Young's inequality
zbMATH Keywords: Minkowski's inequality
zbMATH Keywords: Hölder's inequality
MaRDI profile type: Publication
full work available at URL: s10474-007-6083-9
OpenAlex ID: W2054447383
cites work: Q4039801
cites work: Q5587978
cites work: Q3229647
cites work: Q3483839
cites work: Q4000065
DOI: 10.1007/S10474-007-6083-9
description: scientific article; zbMATH DE number 5368583