Duality theorem over the cone of monotone functions and sequences in higher dimensions

<p/> <p>Let <inline-formula><graphic file="1029-242X-2002-952945-i1.gif"/></inline-formula> be a non-negative function defined on <inline-formula><graphic file="1029-242X-2002-952945-i2.gif"/></inline-formula>. which is monotone in...

Full description

Bibliographic Details
Main Authors: Heinig Hans P, Barza Sorina, Perssona Lars-Erik
Format: Article
Language:English
Published: SpringerOpen 2002-01-01
Series:Journal of Inequalities and Applications
Subjects:
Online Access:http://www.journalofinequalitiesandapplications.com/content/7/952945
_version_ 1811293968856514560
author Heinig Hans P
Barza Sorina
Perssona Lars-Erik
author_facet Heinig Hans P
Barza Sorina
Perssona Lars-Erik
author_sort Heinig Hans P
collection DOAJ
description <p/> <p>Let <inline-formula><graphic file="1029-242X-2002-952945-i1.gif"/></inline-formula> be a non-negative function defined on <inline-formula><graphic file="1029-242X-2002-952945-i2.gif"/></inline-formula>. which is monotone in each variable separately. If <inline-formula><graphic file="1029-242X-2002-952945-i3.gif"/></inline-formula>, <inline-formula><graphic file="1029-242X-2002-952945-i4.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-2002-952945-i5.gif"/></inline-formula> a product weight function, then equivalent expressions for <inline-formula><graphic file="1029-242X-2002-952945-i6.gif"/></inline-formula> are given, where the supremum is taken over all such functions <inline-formula><graphic file="1029-242X-2002-952945-i7.gif"/></inline-formula>.</p> <p>Variants of such duality results involving sequences are also given. Applications involving weight characterizations for which operators defined on such functions (sequences) are bounded in weighted Lebesgue (sequence) spaces are also pointed out.</p>
first_indexed 2024-04-13T05:09:23Z
format Article
id doaj.art-b7e57f5ba4c5445994430edece343800
institution Directory Open Access Journal
issn 1025-5834
1029-242X
language English
last_indexed 2024-04-13T05:09:23Z
publishDate 2002-01-01
publisher SpringerOpen
record_format Article
series Journal of Inequalities and Applications
spelling doaj.art-b7e57f5ba4c5445994430edece3438002022-12-22T03:01:04ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2002-01-0120021952945Duality theorem over the cone of monotone functions and sequences in higher dimensionsHeinig Hans PBarza SorinaPerssona Lars-Erik<p/> <p>Let <inline-formula><graphic file="1029-242X-2002-952945-i1.gif"/></inline-formula> be a non-negative function defined on <inline-formula><graphic file="1029-242X-2002-952945-i2.gif"/></inline-formula>. which is monotone in each variable separately. If <inline-formula><graphic file="1029-242X-2002-952945-i3.gif"/></inline-formula>, <inline-formula><graphic file="1029-242X-2002-952945-i4.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-2002-952945-i5.gif"/></inline-formula> a product weight function, then equivalent expressions for <inline-formula><graphic file="1029-242X-2002-952945-i6.gif"/></inline-formula> are given, where the supremum is taken over all such functions <inline-formula><graphic file="1029-242X-2002-952945-i7.gif"/></inline-formula>.</p> <p>Variants of such duality results involving sequences are also given. Applications involving weight characterizations for which operators defined on such functions (sequences) are bounded in weighted Lebesgue (sequence) spaces are also pointed out.</p>http://www.journalofinequalitiesandapplications.com/content/7/952945Duality theoremsMonotone functionsMultidimensional functionsWeighted inequalities
spellingShingle Heinig Hans P
Barza Sorina
Perssona Lars-Erik
Duality theorem over the cone of monotone functions and sequences in higher dimensions
Journal of Inequalities and Applications
Duality theorems
Monotone functions
Multidimensional functions
Weighted inequalities
title Duality theorem over the cone of monotone functions and sequences in higher dimensions
title_full Duality theorem over the cone of monotone functions and sequences in higher dimensions
title_fullStr Duality theorem over the cone of monotone functions and sequences in higher dimensions
title_full_unstemmed Duality theorem over the cone of monotone functions and sequences in higher dimensions
title_short Duality theorem over the cone of monotone functions and sequences in higher dimensions
title_sort duality theorem over the cone of monotone functions and sequences in higher dimensions
topic Duality theorems
Monotone functions
Multidimensional functions
Weighted inequalities
url http://www.journalofinequalitiesandapplications.com/content/7/952945
work_keys_str_mv AT heinighansp dualitytheoremovertheconeofmonotonefunctionsandsequencesinhigherdimensions
AT barzasorina dualitytheoremovertheconeofmonotonefunctionsandsequencesinhigherdimensions
AT perssonalarserik dualitytheoremovertheconeofmonotonefunctionsandsequencesinhigherdimensions