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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2002-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/7/952945 |
| Summary: | <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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| ISSN: | 1025-5834 1029-242X |