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<p>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.</p>

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Modified Brascamp-Lieb inequalities and log-Sobolev inequalities for one-dimensional log-concave measure

  • 期刊论文

  • 发表日期：

    2025年1月24日

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  • Denghui Wu,
  • Jiazu Zhou

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 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.