Santaló's inequality on n by complex interpolation
Comptes Rendus. Mathématique, Volume 334 (2002) no. 9, pp. 767-772.

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

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.

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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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     title = {Santal\'o's inequality on $ \mathbb{C}^{n}$ by complex interpolation},
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Cordero-Erausquin, Dario. 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. 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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