Euclidean Forward-Reverse Brascamp-Lieb Inequalities: Finiteness, Structure and Extremals
Functional Analysis
2019-08-30 v2 Information Theory
Classical Analysis and ODEs
math.IT
Abstract
A new proof is given for the fact that centered gaussian functions saturate the Euclidean forward-reverse Brascamp-Lieb inequalities, extending the Brascamp-Lieb and Barthe theorems. A duality principle for best constants is also developed, which generalizes the fact that the best constants in the Brascamp-Lieb and Barthe inequalities are equal. Finally, as the title hints, the main results concerning finiteness, structure and gaussian-extremizability for the Brascamp-Lieb inequality due to Bennett, Carbery, Christ and Tao are generalized to the setting of the forward-reverse Brascamp-Lieb inequality.
Keywords
Cite
@article{arxiv.1907.12723,
title = {Euclidean Forward-Reverse Brascamp-Lieb Inequalities: Finiteness, Structure and Extremals},
author = {Thomas A. Courtade and Jingbo Liu},
journal= {arXiv preprint arXiv:1907.12723},
year = {2019}
}
Comments
37 pages, no figures. v2 includes added examples and minor updates to simplify presentation. Comments welcome