Strong Brascamp-Lieb Inequalities
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 -stability. Our proofs in this paper are based on information-theoretic and coupling techniques.
Keywords
Cite
@article{arxiv.2102.06935,
title = {Strong Brascamp-Lieb Inequalities},
author = {Lei Yu},
journal= {arXiv preprint arXiv:2102.06935},
year = {2021}
}
Comments
68 pages, 4 figures. Properties of the two-parameter entropy were added in the introduction, the range of the parameter $(p,\hat{p},q)$ for the single-function version of Brascamp--Lieb inequalities was corrected, many proof details were added, and some typos and minor errors were fixed