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By adapting some ideas of M. Ledoux \cite{ledoux2}, \cite{ledoux-stflour} and\cite{Led} to a sub-Riemannian framework we study Sobolev, Poincar\'e andisoperimetric inequalities associated to subelliptic diffusion operators thatsatisfy the generalized curvature dimension inequality that was introduced byF. Baudoin and N. Garofalo in \cite{Bau2}. Our results apply in particular onall CR Sasakian manifolds whose horizontal Webster-Tanaka-Ricci curvature isnon negative, all Carnot groups with step two, and wide subclasses of principalbundles over Riemannian manifolds whose Ricci curvature is non negative.

Sobolev, Poincare and isoperimetric inequalities for subelliptic diffusion operators satisfying a generalized curvature dimension inequality