Some functional forms of Blaschke-Santaló inequality

Details Some functional forms of Blaschke-Santaló inequality Some functional forms of Blaschke-Santaló inequality

2006-09-20

arxiv.org/abs/math/0609553v1

Mathematics

Functional Analysis

19 pages, to appear in Mathematische Zeitschrift

Scientific paper

We establish new functional versions of the Blaschke-Santal\'o 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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