Santaló's inequality on $ \mathbb{C}^{n}$ by complex interpolation

Dario Cordero-Erausquin

doi:10.1016/S1631-073X(02)02328-2

Santaló's inequality on

ℂ^{n}

by complex interpolation

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

Comptes Rendus. Mathématique, Volume 334 (2002) no. 9, pp. 767-772.

Abstract
Résumé

A new approach to Santaló's inequality on $ℂ^{n}$ 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.

Received: 2002-02-13
Accepted: 2002-02-19
Published online: 2002-01-01

DOI: 10.1016/S1631-073X(02)02328-2

Author's affiliations:

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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     title = {Santal\'o's inequality on $ \mathbb{C}^{n}$ by complex interpolation},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {767--772},
     publisher = {Elsevier},
     volume = {334},
     number = {9},
     year = {2002},
     doi = {10.1016/S1631-073X(02)02328-2},
     language = {en},
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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/

References
Cited by

[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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