This is an announcement for the paper "Some functional forms of Blaschke-Santal'o inequality" by Matthieu Fradelizi and Mathieu Meyer.
Abstract: 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.
Archive classification: Functional Analysis; Metric Geometry
Mathematics Subject Classification: 52A40
Remarks: 19 pages, to appear in Mathematische Zeitschrift
The source file(s), Blaschke-Santalo-final.tex: 48038 bytes, is(are) stored in gzipped form as 0609553.gz with size 15kb. The corresponding postcript file has gzipped size 71kb.
Submitted from: matthieu.fradelizi@univ-mlv.fr
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