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

[21] Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation [J].

Figalli, A. ;

Maggi, F. ;

Pratelli, A. .

ADVANCES IN MATHEMATICS, 2013, 242 :80-101

[22] Log-Sobolev Inequalities for Infinite-Dimensional Gibbs Measures with Non-Quadratic Interactions [J].

Inglis, James ;

Papageorgiou, Ioannis .

MARKOV PROCESSES AND RELATED FIELDS, 2019, 25 (05) :879-897

[23] Log-Sobolev inequalities for subelliptic operators satisfying a generalized curvature dimension inequality [J].

Baudoin, Fabrice ;

Bonnefont, Michel .

JOURNAL OF FUNCTIONAL ANALYSIS, 2012, 262 (06) :2646-2676

[24] Direct and reverse log-Sobolev inequalities in μ-deformed segal-bargmai analysis [J].

Aguila, Carlos Ernesto Angulo ;

Sontz, Stephen Bruce .

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2007, 10 (04) :539-571

[25] Functional inequalities for perturbed measures with applications to log-concave measures and to some Bayesian problems [J].

Cattiaux, Patrick ;

Guillin, Arnaud .

BERNOULLI, 2022, 28 (04) :2294-2321

[26] Sharp Moment-Entropy Inequalities and Capacity Bounds for Symmetric Log-Concave Distributions [J].

Madiman, Mokshay ;

Nayar, Piotr ;

Tkocz, Tomasz .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2021, 67 (01) :81-94

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