Convex conjugates of integral functionals
type: Item
instance of: scholarly article
title: Convex conjugates of integral functionals
zbMATH Open document ID: 0997.52008
DOI: 10.1023/A:1017943805248
published in: Acta Mathematica Hungarica
publication date: 2002-11-03T00:00:00Z
review text: Having a measure space \((\Omega ,{\mathcal A},R),\) \(\gamma :{\mathbf R} \rightarrow [0,\infty [\) a convex function with \(\gamma (0)=0\) and \(V\) a vector space of measurable functions, the author is interested in the \(\sigma (V^{\ast \ast },V^{\ast })\)-l.s.c. regularization of the integral convex functional \(I_{\gamma }:V\rightarrow [0,\infty ]\) defined by \(I_{\gamma }(v)=\int_{\Omega }\gamma (v(\omega)) R(d\omega),\) where \(V^{\ast }\) and \(V^{\ast \ast }\) are the algebraic dual and bidual of \( V.\) In order to do this, the author studies the algebraic biconjugate of restricted functions, the conjugate on Riesz spaces and duality in Orlicz spaces.
Mathematics Subject Classification ID: 52A41
Mathematics Subject Classification ID: 26B25
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46B10
zbMATH DE Number: 1822359
zbMATH Keywords: convex integral functionals
zbMATH Keywords: convex conjugacy
zbMATH Keywords: Orlicz spaces
zbMATH Keywords: Riesz spaces
zbMATH Keywords: duality and reflexivity
author: Christian Léonard
reviewed by: Constantin Zălinescu
MaRDI profile type: Publication
full work available at URL: a:1017943805248
OpenAlex ID: W1561838142
description: scientific article; zbMATH DE number 1822359