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 26 条

[11] A characterization of a class of convex log-Sobolev inequalities on the real line
Shu, Yan
Strzelecki, Michal
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2018, 54 (04): : 2075 - 2091
[12] Dimension-free log-Sobolev inequalities for mixture distributions
Chen, Hong-Bin
Chewi, Sinho
Niles-Weed, Jonathan
JOURNAL OF FUNCTIONAL ANALYSIS, 2021, 281 (11)
[13] Log-Sobolev and Nash Inequalities for Discrete-Time Finite Markov Chains
Song, Yan-Hong
MARKOV PROCESSES AND RELATED FIELDS, 2015, 21 (01) : 127 - 144
[14] A simple proof of log-Sobolev inequalities on a path space with Gibbs measures
Kawabi, H
INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2006, 9 (02) : 321 - 329
[15] Time-uniform log-Sobolev inequalities and applications to propagation of chaos
Monmarche, Pierre
Ren, Zhenjie
Wang, Songbo
ELECTRONIC JOURNAL OF PROBABILITY, 2024, 29
[16] Sharp log-Sobolev inequalities in CD(0, N) spaces with applications
Balogh, Zoltan M.
Kristaly, Alexandru
Tripaldi, Francesca
JOURNAL OF FUNCTIONAL ANALYSIS, 2024, 286 (02)
[17] Dimensional variance inequalities of Brascamp-Lieb type and a local approach to dimensional Prekopa's theorem
Van Hoang Nguyen
JOURNAL OF FUNCTIONAL ANALYSIS, 2014, 266 (02) : 931 - 955
[18] Riemannian metrics on convex sets with applications to Poincare and log-Sobolev inequalities
Kolesnikov, Alexander V.
Milman, Emanuel
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2016, 55 (04)
[19] CONCENTRATION INEQUALITIES FOR LOG-CONCAVE DISTRIBUTIONS WITH APPLICATIONS TO RANDOM SURFACE FLUCTUATIONS
Magazinov, Alexander
Peled, Ron
ANNALS OF PROBABILITY, 2022, 50 (02) : 735 - 770
[20] The first variation of the total mass of log-concave functions and related inequalities
Colesanti, Andrea
Fragala, Ilaria
ADVANCES IN MATHEMATICS, 2013, 244 : 708 - 749

← 1 2 3 →