Sobolev embeddings for kinetic Fokker-Planck equations

We introduce intrinsic Sobolev-Slobodeckij spaces for a class of ultra-parabolic Kolmogorov type operators satisfying the weak Hörmander condition. We show continuous embeddings into Lorentz and intrinsic Hölder spaces, as well as approximation and interpolation inequalities by means of an intrinsic Taylor expansion, extending analogous results for Hölder spaces.