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

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doi:10.1007/s10473-025-0108-8

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

CLC Number:

52A20

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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