Transport proofs of some functional inverse Santal{\'o} inequalities
Functional Analysis
2021-09-10 v3
Abstract
In this paper, we present a simple proof of a recent result of the second author which establishes that functional inverse-Santal{\'o} inequalities follow from Entropy-Transport inequalities. Then, using transport arguments together with elementary correlation inequalities, we prove these sharp Entropy-Transport inequalities in dimension 1. We also revisit the proof of the functional inverse-Santal{\'o} inequalities in the n dimensional unconditional case using these ideas.
Keywords
Cite
@article{arxiv.2109.00871,
title = {Transport proofs of some functional inverse Santal{\'o} inequalities},
author = {Matthieu Fradelizi and Nathael Gozlan and Simon Zugmeyer},
journal= {arXiv preprint arXiv:2109.00871},
year = {2021}
}