Comptes Rendus
no. 1
Functional analysis/Probability theory
A refinement of the Brascamp–Lieb–Poincaré inequality in one dimension

Présenté par : Jean-Pierre Kahane

Ionel Popescu1, 2
1 School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA 30332, USA
2 “Simion Stoilow” Institute of Mathematics of Romanian Academy, 21 Calea Griviţei, Bucharest, Romania
Comptes Rendus. Mathématique, Volume 352 (2014) no. 1, pp. 55-58.

Dans cette brève Note, on donne un raffinement de lʼinégalité de Brascamp–Lieb [1] dans le style de lʼextension de Houdré–Kagan [3] pour lʼinégalité de Poincaré en une dimension. Cette Note est inspirée par les travaux de Helffer et de Ledoux.

In this short note, we give a refinement of the Brascamp–Lieb inequality in the style of the Houdré–Kagan extension for the Poincaré inequality in one dimension. This is inspired by works by Helffer and by Ledoux.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.11.013
Ionel Popescu 1, 2

1 School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA 30332, USA
2 “Simion Stoilow” Institute of Mathematics of Romanian Academy, 21 Calea Griviţei, Bucharest, Romania 
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Ionel Popescu. A refinement of the Brascamp–Lieb–Poincaré inequality in one dimension. Comptes Rendus. Mathématique, Volume 352 (2014) no. 1, pp. 55-58. doi : 10.1016/j.crma.2013.11.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.11.013/

[1] H.J. Brascamp; E.H. Lieb On extensions of the Brunn–Minkowski and Prékopa–Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation, J. Funct. Anal., Volume 22 (1976) no. 4, pp. 366-389

[2] B. Helffer Remarks on decay of correlations and Witten Laplacians, Brascamp–Lieb inequalities and semiclassical limit, J. Funct. Anal., Volume 155 (1998) no. 2, pp. 571-586

[3] C. Houdré; A. Kagan Variance inequalities for functions of Gaussian variables, J. Theor. Probab., Volume 8 (1995) no. 1, pp. 23-30

[4] M. Ledoux Lʼalgèbre de Lie des gradients itérés dʼun générateur markovien – Développements de moyennes et entropies, Ann. Sci. Éc. Norm. Super. (4), Volume 28 (1995) no. 4, pp. 435-460

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