Santaló's inequality on n by complex interpolation
[Inégalité de Santaló sur n par interpolation complexe]
Comptes Rendus. Mathématique, Tome 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.

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DOI : 10.1016/S1631-073X(02)02328-2
Cordero-Erausquin, Dario 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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Cordero-Erausquin, Dario. Santaló's inequality on $ \mathbb{C}^{n}$ by complex interpolation. Comptes Rendus. Mathématique, Tome 334 (2002) no. 9, pp. 767-772. doi : 10.1016/S1631-073X(02)02328-2. http://www.numdam.org/articles/10.1016/S1631-073X(02)02328-2/

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

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

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

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

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

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

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