Semi-groupes d'opérateurs et espaces fonctionnels sur les groupes de Lie

We prove imbedding theorems in the setting of abstract symmetric sub-markovian semi-groups, under some natural dimensional hypothesis. Our results are sharp and extend classical ones. They involve Lipschitz, Besov, and Sobolev spaces, as well as Lebesgue spaces, and include a generalization of the Herz-Bernstein Theorem on the Wiener algebra. They typically apply to function spaces associated to left invariant sub-laplacians on unimodular Lie groups, thanks to estimates obtained by Varopoulos.