Some functional forms of Blaschke–Santaló inequality

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 t...

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Bibliographic Details
Published inMathematische Zeitschrift Vol. 256; no. 2; pp. 379 - 395
Main Authors Fradelizi, M., Meyer, M.
Format Journal Article
LanguageEnglish
Published Springer 01.06.2007
Subjects
Mathematical Physics
Mathematics
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Summary: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.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-006-0078-z