sur les fonctions extremales des inegalites de Sobolev des operateurs de diffusion

摘要

We use a dimension-curvature criterion introduced by D. Bakry and M. Emery [B-El] to study the extremal functions related to Sobolev-type inequalities for families of diffusion operatorscovering in particular, the Ornstein-Uhlenbeck generator, the spherical Laplacian, as well as the multidimensional Gegenbauer operators.