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
收藏
页码：104 / 117
页数：14
相关论文
共 26 条
  • [1] MODIFIED LOG-SOBOLEV INEQUALITIES FOR STRONGLY LOG-CONCAVE DISTRIBUTIONS
    Cryan, Mary
    Guo, Heng
    Mousa, Giorgos
    ANNALS OF PROBABILITY, 2021, 49 (01) : 506 - 525
  • [2] Asymmetric covariance estimates of Brascamp-Lieb type and related inequalities for log-concave measures
    Carlen, Eric A.
    Cordero-Erausquin, Dario
    Lieb, Elliott H.
    ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2013, 49 (01): : 1 - 12
  • [3] DIMENSIONAL IMPROVEMENTS OF THE LOGARITHMIC SOBOLEV, TALAGRAND AND BRASCAMP-LIEB INEQUALITIES
    Bolley, Francois
    Gentil, Ivan
    Guillin, Arnaud
    ANNALS OF PROBABILITY, 2018, 46 (01) : 261 - 301
  • [4] Modified log-Sobolev inequalities, Beckner inequalities and moment estimates
    Adamczak, Radoslaw
    Polaczyk, Bartlomiej
    Strzelecki, Michal
    JOURNAL OF FUNCTIONAL ANALYSIS, 2022, 282 (07)
  • [5] On matrix-valued log-concavity and related Prekopa and Brascamp-Lieb inequalities
    Cordero-Erausquin, Dario
    ADVANCES IN MATHEMATICS, 2019, 351 : 96 - 116
  • [6] Poincare and Log-Sobolev Inequalities for Mixtures
    Schlichting, Andre
    ENTROPY, 2019, 21 (01):
  • [7] LOG-SOBOLEV INEQUALITIES: DIFFERENT ROLES OF RIC AND HESS
    Wang, Feng-Yu
    ANNALS OF PROBABILITY, 2009, 37 (04) : 1587 - 1604
  • [8] Transport Inequalities for Log-concave Measures, Quantitative Forms, and Applications
    Cordero-Erausquin, Dario
    CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2017, 69 (03): : 481 - 501
  • [9] Geometric and Functional Inequalities for Log-Concave Probability Sequences
    Marsiglietti, Arnaud
    Melbourne, James
    DISCRETE & COMPUTATIONAL GEOMETRY, 2024, 71 (02) : 556 - 586
  • [10] The Deficit in the Gaussian Log-Sobolev Inequality and Inverse Santalo Inequalities
    Gozlan, Nathael
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2022, 2022 (17) : 13396 - 13446
123