论文信息 - Some extensions of the Pr\'ekopa-Leindler inequality using Borell's stochastic approach

Some extensions of the Pr\'ekopa-Leindler inequality using Borell's stochastic approach

We present an abstract form of the Pr\'ekopa-Leindler inequality that includes several known -and a few new- related functional inequalities on Euclidean spaces. The method of proof and also the formulation of the new inequalities are based on Christer Borell's stochastic approach to Brunn-Minkowski type inequalities.

Dario Cordero-Erausquin | Bernard Maurey

[1] C. Borell. Convex set functions ind-space , 1975 .

[2] F. Barthe. On a reverse form of the Brascamp-Lieb inequality , 1997, math/9705210.

[3] C. Borell,et al. Diffusion Equations and Geometric Inequalities , 2000 .

[4] V. V. Buldygin,et al. Brunn-Minkowski inequality , 2000 .

[5] D. Cordero-Erausquin. On Berndtsson’s generalization of Prékopa’s theorem , 2005 .

[6] J. K. Hunter,et al. Measure Theory , 2007 .

[7] Inégalité de Brunn-Minkowski-Lusternik, et autres inégalités géométriques et fonctionnelles , 2004 .

[8] R. McCann. A Convexity Principle for Interacting Gases , 1997 .

[9] B. Berndtsson. Prekopa's theorem and Kiselman's minimum principle for plurisubharmonic functions , 1998 .

[10] Joseph Lehec. Short Probabilistic Proof of the Brascamp-Lieb and Barthe Theorems , 2014, Canadian Mathematical Bulletin.

[11] B. Maurey. Some deviation inequalities , 1990, math/9201216.

[12] F. Barthe. A Continuous Version of the Brascamp-Lieb Inequalities , 2004 .