POINCARÉ AND LOGARITHMIC SOBOLEV INEQUALITIES FOR NEARLY RADIAL MEASURES

Patrick Cattiaux (1) , Arnaud Guillin (2) , Li Ming Wu

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 LMBP - Laboratoire de Mathématiques Blaise Pascal

If Poincaré inequality has been studied by Bobkov for radial measures, few is known about the logarithmic Sobolev inequalty in the radial case. We try to fill this gap here using different methods: Bobkov's argument and super-Poincaré inequalities, direct approach via L1-logarithmic Sobolev inequalities. We also give various examples where the obtained bounds are quite sharp. Recent bounds obtained by Lee-Vempala in the logconcave bounded case are refined for radial measures.

Mots clés: radial measure; logconcave measure; Poincaré inequality; logarithmic Sobolev inequality; Super-Poincaré inequality

Domaines: Probabilités [math.PR]; Analyse fonctionnelle [math.FA]

Patrick Cattiaux, Arnaud Guillin, Li Ming Wu. POINCARÉ AND LOGARITHMIC SOBOLEV INEQUALITIES FOR NEARLY RADIAL MEASURES. Acta Mathematica Sinica English Series, 2022, 38 (8), pp.1377-1398. ⟨10.1007/s10114-022-0501-3⟩. ⟨hal-02418658⟩