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.
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
.
DOI: 10.1007/s10473-025-0108-8
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