Increasing functions and inverse Santalo inequality for unconditional functions

作     者：Fradelizi, Matthieu Meyer, Mathieu 

作者机构：Univ Marne La Vallee Lab Anal & Math Appl UMR 8050 F-77454 Champs Sur Marne 2 Marne La Valle France 

出 版 物：《POSITIVITY》 (正性)

年 卷 期：2008年第12卷第3期

页      面：407-420页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：increasing functions Legendre transform inverse-Santalo inequality 

摘      要：Let phi : R(n) - R boolean OR {+infinity} be a convex function and L phi be its Legendre tranform. It is proved that if phi is invariant by changes of signs, then integral e(-phi) integral e(-L phi) = 4(n). This is a functional version of the inverse Santalo inequality for unconditional convex bodies due to J. Saint Raymond. The proof involves a general result on increasing functions on R(n) x R(n) together with a functional form of Lozanovskii s lemma. In the last section, we prove that for some c 0, one has always integral e-(phi) integral e(-L phi) = c(n). This generalizes a result of B. Klartag and V. Milman.