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Pré-Publication, Document De Travail Année : 2021

Transport proofs of some functional inverse Santaló inequalities

Résumé

In this paper, we present a simple proof of a recent result of the second author which establishes that functional inverse-Santaló 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-Santaló inequalities in the n dimensional unconditional case using these ideas.
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Dates et versions

hal-03284636 , version 1 (12-07-2021)
hal-03284636 , version 2 (02-09-2021)
hal-03284636 , version 3 (08-09-2021)

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Matthieu Fradelizi, Nathael Gozlan, Simon Zugmeyer. Transport proofs of some functional inverse Santaló inequalities. 2021. ⟨hal-03284636v2⟩
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