Displaying similar documents to “Hypercontractivity for perturbed diffusion semigroups”

From the Prékopa-Leindler inequality to modified logarithmic Sobolev inequality

Ivan Gentil (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

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We develop in this paper an improvement of the method given by S. Bobkov and M. Ledoux in [BL00]. Using the Prékopa-Leindler inequality, we prove a modified logarithmic Sobolev inequality adapted for all measures on ℝ n , with a strictly convex and super-linear potential. This inequality implies modified logarithmic Sobolev inequality, developed in [GGM05, GGM07], for all uniformly strictly convex potential as well as the Euclidean logarithmic Sobolev inequality.