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Some functional forms of Blaschke-Santaló inequality

Matthieu Fradelizi·Mathieu Meyer
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Abstract

We establish new functional versions of the Blaschke-Santaló inequality on the volume product of a convex body which generalize to the non-symmetric setting an inequality of K. Ball and we give a simple proof of the case of equality. As a corollary, we get some inequalities for $\log$-concave functions and Legendre transforms which extend the recent result of Artstein, Klartag and Milman, with its equality case.

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Matthieu Fradelizi, Mathieu Meyer. 2006-09-20. Some functional forms of Blaschke-Santaló inequality. https://arxiv.org/abs/math/0609553

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