Some functional forms of Blaschke-Santalo inequality

Matthieu Fradelizi (1) , M. Meyer

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We establish new functional versions of the Blaschke-Santalo inequality on the volume product of a convex body which generalize to the non-symmetric setting an inequality of Ball [Isometric problems in Ep and sections of convex sets. PhD Dissertation, Cambridge, 1986] 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 et al. [Mathematika 51:33-48, 2004], with its equality case.

Domaines: Physique mathématique [math-ph]

Matthieu Fradelizi, M. Meyer. Some functional forms of Blaschke-Santalo inequality. Mathematische Zeitschrift, 2007, 256 (2), pp.379--395. ⟨10.1007/s00209-006-0078-z⟩. ⟨hal-00693088⟩