Averaging operators on decreasing or positive functions: equivalence and optimal bounds

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Title:	Averaging operators on decreasing or positive functions: equivalence and optimal bounds
Author:	Boza Rocho, Santiago; Soria de Diego, Javier
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. LARCA - Laboratori d'Algorísmia Relacional, Complexitat i Aprenentatge
Abstract:	We study the optimal bounds for the Hardy operator S minus the identity, as well as S and its dualoperator S*, on the full range 1 = p = 8, for the cases of decreasing, positive or general functions (infact, these two kinds of inequalities are equivalent for the appropriate cone of functions). For 1< p = 2, we prove that all these estimates are the same, but for 2 < p <8, they exhibit a completely different behavior.
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica -Mathematical analysis -Hardy operator -dual operator -best constants -decreasing functions -Anàlisi matemàtica
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Document type:	Article - Submitted version Article
Published by:	Elsevier
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