Comptes Rendus
Santaló's inequality on n by complex interpolation
[Inégalité de Santaló sur n par interpolation complexe]
Comptes Rendus. Mathématique, Volume 334 (2002) no. 9, pp. 767-772.

On donne une nouvelle approche de l'inégalité de Santaló en combinant l'interpolation complexe et la généralisation de l'inégalité de Prékopa obtenue par Berntdsson.

A new approach to Santaló's inequality on n is obtained by combining complex interpolation and Berndtsson's generalization of Prékopa's inequality.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02328-2

Dario Cordero-Erausquin 1

1 Laboratoire d'analyse et de mathématiques appliquées (CNRS UMR 8050), Université de Marne la Vallée, 77454 Marne la Vallée cedex 2, France
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Dario Cordero-Erausquin. Santaló's inequality on $ \mathbb{C}^{n}$ by complex interpolation. Comptes Rendus. Mathématique, Volume 334 (2002) no. 9, pp. 767-772. doi : 10.1016/S1631-073X(02)02328-2. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02328-2/

[1] J. Bergh; J. Löftröm Interpolation Spaces. An Introduction, Springer, Berlin, 1976

[2] B. Berndtsson Prekopa's theorem and Kiselman's minimum principle for plurisubharmonic functions, Math. Ann., Volume 312 (1998), pp. 785-792

[3] L. Hörmander An Introduction to Complex Analysis in Several Variables, North-Holland, Amsterdam, 1990

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

[5] A. Prékopa On logarithmic concave measures and functions, Acta Sci. Math. (Szeged), Volume 34 (1973), pp. 335-343

[6] L. Santaló Un invariante afin para los cuerpos convexos del espacio de n dimensiones, Portugal Math., Volume 8 (1949), pp. 155-1961

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