Rogers-Shephard inequality for log-concave functions

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• 作者：David Alonso-Gutié ; rrez^a ; ^{alonsod@unizar.es" class="auth_mail" title="E-mail the corresponding author} ; Bernardo Gonzá ; lez Merino^b ; ^{bg.merino@tum.de" class="auth_mail" title="E-mail the corresponding author} ; C. Hugo Jimé ; nez^c ; ^{hugojimenez@mat.puc-rio.br" class="auth_mail" title="E-mail the corresponding author} ; Rafael Villa^d ; ^{villa@us.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 52A20 ; secondary ; 39B62 ; 46N10
• 刊名：Journal of Functional Analysis
• 出版年：2016
• 出版时间：1 December 2016
• 年：2016
• 卷：271
• 期：11
• 页码：3269-3299
• 全文大小：508 K

文摘

In this paper we prove different functional inequalities extending the classical Rogers–Shephard inequalities for convex bodies. The original inequalities provide an optimal relation between the volume of a convex body and the volume of several symmetrizations of the body, such as, its difference body. We characterize the equality cases in all these inequalities. Our method is based on the extension of the notion of a convolution body of two convex sets to any pair of log-concave functions and the study of some geometrical properties of these new sets.