A direct proof of the functional Santaló inequality

Joseph Lehec

doi:10.1016/j.crma.2008.11.015

Functional Analysis

A direct proof of the functional Santaló inequality

Presented by: Gilles Pisier

Joseph Lehec ¹

¹ Université Paris-Est, Laboratoire d'analyse et de mathématiques appliquées, cité Descartes, 5, boulevard Descartes, 77454 Marne la Vallée cedex 2, France

Comptes Rendus. Mathématique, Volume 347 (2009) no. 1-2, pp. 55-58.

Abstract
Résumé

We give a simple proof of a functional version of the Blaschke–Santaló inequality due to Artstein, Klartag and Milman. The proof is by induction on the dimension and does not use the Blaschke–Santaló inequality.

On présente une démonstration simple d'une version fonctionnelle de l'inégalité de Blaschke–Santaló, due à Artstein, Klartag et Milman. On procède par récurrence sur la dimension, sans faire appel à l'inégalité ensembliste.

Received: 2008-11-04
Accepted: 2008-11-24
Published online: 2008-12-18

DOI: 10.1016/j.crma.2008.11.015

Author's affiliations:

Joseph Lehec ¹

¹ Université Paris-Est, Laboratoire d'analyse et de mathématiques appliquées, cité Descartes, 5, boulevard Descartes, 77454 Marne la Vallée cedex 2, France

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Joseph Lehec. A direct proof of the functional Santaló inequality. Comptes Rendus. Mathématique, Volume 347 (2009) no. 1-2, pp. 55-58. doi : 10.1016/j.crma.2008.11.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.11.015/

References
Cited by

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[2] K. Ball, Isometric problems in $ℓ_{p}$ and sections of convex sets, Doctoral thesis, University of Cambridge, 1986

[3] K. Ball An elementary introduction to modern convex geometry (S. Levy, ed.), Flavors of Geometry, Cambridge University Press, 1997

[4] M. Fradelizi; M. Meyer Some functional forms of Blaschke–Santaló inequality, Math. Z., Volume 256 (2007) no. 2, pp. 379-395

[5] J. Lehec, Partitions and functional Santaló inequalities, Arch. Math. (Basel) (2008), in press

[6] E. Lutwak Extended affine surface area, Adv. Math., Volume 85 (1991) no. 1, pp. 39-68

[7] M. Meyer; A. Pajor On the Blaschke Santaló inequality, Arch. Math. (Basel), Volume 55 (1990), pp. 82-93

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