Modified Brascamp-Lieb inequalities and log-Sobolev inequalities for one-dimensional log-concave measure

被引：0

作者：

Wu, Denghui ^{[1
]}

Zhou, Jiazu ^{[2
]}

机构：

[1] Northwest A&F Univ, Coll Sci, Yangling 712100, Peoples R China

[2] Guizhou Educ Univ, Sch Math & Big Data, Guiyang 550018, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2025年 / 45卷 / 01期

关键词：

Brunn-Minkowski inequality; Pr & eacute; kopa-Leindler inequality; Brascamp-Lieb inequality; log-Sobolev inequality; log-concave measure; BRUNN-MINKOWSKI; LOGARITHMIC SOBOLEV; STABILITY;

D O I：

10.1007/s10473-025-0108-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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 Pr & eacute;kopa-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.

引用

页码：104 / 117

页数：14

共 50 条

[11] Sharp Log-Sobolev inequalities
Rothaus, OS
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 126 (10) : 2903 - 2904
[12] Harnack inequalities for log-Sobolev functions and estimates of log-Sobolev constants
Wang, FY
ANNALS OF PROBABILITY, 1999, 27 (02): : 653 - 663
[13] MOMENT ESTIMATES IMPLIED BY MODIFIED LOG-SOBOLEV INEQUALITIES
Adamczak, Radoslaw
Bednorz, Witold
Wolff, Pawel
ESAIM-PROBABILITY AND STATISTICS, 2018, 21 : 467 - 494
[14] Poincare and Log-Sobolev Inequalities for Mixtures
Schlichting, Andre
ENTROPY, 2019, 21 (01):
[15] A generalization of poincaré and log-Sobolev inequalities
Wang F.-Y.
Potential Analysis, 2005, 22 (1) : 1 - 15
[16] On matrix-valued log-concavity and related Prekopa and Brascamp-Lieb inequalities
Cordero-Erausquin, Dario
ADVANCES IN MATHEMATICS, 2019, 351 : 96 - 116
[17] Some inequalities derived from log-Sobolev inequalities
Rothaus, OS
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 125 (12) : 3601 - 3603
[18] Fractional Log-Sobolev Inequalities on the Sphere
Tang, Hanli
Zhang, Caifeng
JOURNAL OF GEOMETRIC ANALYSIS, 2025, 35 (05)
[19] A Generalization of Poincaré and Log-Sobolev Inequalities
Feng-Yu Wang
Potential Analysis, 2005, 22 (1) : 1 - 15
[20] A generalization of Poincare and log-Sobolev inequalities
Wang, FY
POTENTIAL ANALYSIS, 2005, 22 (01) : 1 - 15

← 1 2 3 4 5 →