Sobolev and Morrey estimates for non-smooth vector fields of step two (Q1607603)

Summary: We prove Sobolev-type and Morrey-type inequalities for Sobolev spaces related to a family of non-smooth vector fields which formally satisfy the Hörmander condition of step 2. The coefficients of the vector fields are not regular enough to define the Carnot-Carathéodory distance. Thus the result is proved by developing a real analysis technique which is based on an approximation procedure of Lipschitz continuous vector fields with a family of left-invariant first order operators on a nilpotent Lie group.