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arXiv · 2102.06935

Strong Brascamp-Lieb Inequalities

Lei Yu
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Abstract

In this paper, we derive sharp nonlinear dimension-free Brascamp--Lieb inequalities (including hypercontractivity inequalities) for distributions on Polish spaces, which strengthen the classic Brascamp--Lieb inequalities. Applications include the extension of Mrs. Gerber's lemma to the cases of R\'enyi divergences and distributions on Polish spaces, the strengthening of small-set expansion theorems, and the characterization of the exponent of the $q$-stability. Our proofs in this paper are based on information-theoretic and coupling techniques.

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BibTeXRIS

Lei Yu. 2021-02-13. Strong Brascamp-Lieb Inequalities. https://arxiv.org/abs/2102.06935

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