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Transport proofs of some functional inverse Santal{o} inequalities

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 Added by Simon Zugmeyer
 Publication date 2021
  fields
and research's language is English




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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.



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