A direct proof of the functional Santalo inequality

TL;DR

This paper provides a straightforward, inductive proof of a functional version of the Blaschke-Santalo inequality, avoiding the traditional reliance on the inequality itself.

Contribution

It introduces a new, simple proof method for the functional Santalo inequality that bypasses the need for the inequality's prior use.

Findings

Proof is simple and inductive

Avoids using the original inequality

Applicable to functional versions

Abstract

We give a simple proof of a functional version of the Blaschke-Santalo inequality due to Artstein, Klartag and Milman. The proof is by induction on the dimension and does not use the Blaschke-Santalo inequality.