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...
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Format: | Article |
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SpringerOpen
2002-01-01
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Series: | Journal of Inequalities and Applications |
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Online Access: | http://www.journalofinequalitiesandapplications.com/content/7/952945 |
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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> |
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institution | Directory Open Access Journal |
issn | 1025-5834 1029-242X |
language | English |
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publishDate | 2002-01-01 |
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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 |
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