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

doi:10.1007/s10473-025-0108-8

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (1): 104-117.doi: 10.1007/s10473-025-0108-8

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

Denghui Wu¹, Jiazu Zhou^2,*

1. College of Science, Northwest A&F University, Yangling 712100, China;
2. School of Mathematics and Big Data, Guizhou Education University, Guiyang 550018, China

收稿日期:2024-08-19 发布日期:2025-02-06
通讯作者: *Jiazu Zhou, E-mail,: zhoujz@gznc.edu.cn
作者简介:Denghui Wu, E-mail,: wudenghui66@163.com
基金资助:
NSFC (12071378, 12461009), the Natural Science Basic Research Program of Shaanxi (2023-JC-YB-036) and the Shaanxi Fundamental Science Research Project for Mathematics and Physics (23JSQ033).

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

Denghui Wu¹, Jiazu Zhou^2,*

1. College of Science, Northwest A&F University, Yangling 712100, China;
2. School of Mathematics and Big Data, Guizhou Education University, Guiyang 550018, China

Received:2024-08-19 Published:2025-02-06
Contact: *Jiazu Zhou, E-mail,: zhoujz@gznc.edu.cn
About author:Denghui Wu, E-mail,: wudenghui66@163.com
Supported by:
NSFC (12071378, 12461009), the Natural Science Basic Research Program of Shaanxi (2023-JC-YB-036) and the Shaanxi Fundamental Science Research Project for Mathematics and Physics (23JSQ033).

摘要/Abstract

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

Abstract: 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.

Key words: Brunn-Minkowski inequality, Prékopa-Leindler inequality, Brascamp-Lieb inequality, log-Sobolev inequality, log-concave measure

中图分类号:

52A20

Denghui Wu, Jiazu Zhou. MODIFIED BRASCAMP-LIEB INEQUALITIES AND LOG-SOBOLEV INEQUALITIES FOR ONE-DIMENSIONAL LOG-CONCAVE MEASURE[J]. 数学物理学报(英文版), 2025, 45(1): 104-117.

Denghui Wu, Jiazu Zhou. MODIFIED BRASCAMP-LIEB INEQUALITIES AND LOG-SOBOLEV INEQUALITIES FOR ONE-DIMENSIONAL LOG-CONCAVE MEASURE[J]. Acta mathematica scientia,Series B, 2025, 45(1): 104-117.

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

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

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