MODIFIED BRASCAMP-LIEB INEQUALITIES AND LOG-SOBOLEV INEQUALITIES FOR ONE-DIMENSIONAL LOG-CONCAVE MEASURE  

作　　者：Denghui WU Jiazu ZHOU 武登辉;周家足(College of Science,Northwest A&F University,Yangling,712100,China;School of Mathematics and Big Data,Guizhou Education University,Guiyang,550018,China)

机构地区：[1]College of Science,Northwest A&F University,Yangling,712100,China [2]School of Mathematics and Big Data,Guizhou Education University,Guiyang,550018,China

出　　处：《Acta Mathematica Scientia》2025年第1期104-117,共14页数学物理学报(B辑英文版)

基　　金：Supported in part by the NSFC(12071378,12461009);the Natural Science Basic Research Program of Shaanxi(2023-JC-YB-036);the Shaanxi Fundamental Science Research Project for Mathematics and Physics(23JSQ033).

摘　　要：In this paper,we develop Maurey’s and Bobkov-Ledoux’s methods to prove modified Brascamp-Lieb inequalities and log-Sobolev inequalities for one-dimensional log-concave measure.To prove these inequalities,the harmonic Prékopa-Leindler inequality is used.We prove that these new inequalities are more efficient in estimating the variance and entropy for some functions with exponential terms.

关 键 词：Brunn-Minkowski inequality Prékopa-Leindler inequality Brascamp-Lieb inequality log-Sobolev inequality log-concave measure 

分 类 号：O17[理学—数学]