The symmetric property (\tau ) for the Gaussian measure

Joseph Lehec (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We give a proof, based on the Poincaré inequality, of the symmetric property (τ) for the Gaussian measure. If f : R d → R is continuous, bounded from below and even, we define Hf (x) = inf y f (x + y) + 1 2 |y| 2 and we have ∫ e^−f dγ d ∫ e Hf dγ d ≤ 1. This property is equivalent to a certain functional form of the Blaschke-Santaló inequality, as explained in a paper by Artstein, Klartag and Milman.

Mots clés: Inégalités fonctionnelles

Domaines: Analyse fonctionnelle [math.FA]

Joseph Lehec. The symmetric property (\tau ) for the Gaussian measure. Annales de la Faculté des Sciences de Toulouse. Mathématiques., 2008, 17 (2), pp.357-370. ⟨10.5802/afst.1186⟩. ⟨hal-00365774⟩