Some functional forms of Blaschke-Santaló inequality
نویسنده
چکیده
We establish new functional versions of the Blaschke-Santaló inequality on the volume product of a convex body which generalize to the nonsymmetric setting an inequality of K. Ball [2] and we give a simple proof of the case of equality. As a corollary, we get some inequalities for logconcave functions and Legendre transforms which extend the recent result of Artstein, Klartag and Milman [1], with its equality case. Université de Marne la Vallée, Laboratoire d’Analyse et de Mathématiques Appliquées (UMR 8050) Cité Descartes 5, Bd Descartes Champs-sur-Marne 77454 Marne la Vallée Cedex 2, France Email: [email protected], [email protected] Fax: 33 1 60 95 75 45
منابع مشابه
A Fourier Analytic Proof of the Blaschke-santaló Inequality
The Blaschke-Santaló Inequality is the assertion that the volume product of a centrally symmetric convex body in Euclidean space is maximized by (and only by) ellipsoids. In this paper we give a Fourier analytic proof of this fact.
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