Function spaces and trace theorems for maximally subelliptic boundary value problems

We introduce Besov and Triebel–Lizorkin spaces on a manifold with boundary adapted to Hörmander vector fields, near a so-called non-characteristic point of the boundary. We prove sharp results in these spaces for the corresponding restriction and trace operators, show these operators are retractions, and other related results. This is the second paper in a forthcoming series devoted to a general theory of maximally subelliptic boundary value problems, and lays the function space foundation for this general theory.