The trace problem for Sobolev spaces over the Heisenberg group

Abstract

This article deals with microlocally weighted Sobolev spaces over the Heisenberg group ℍd, in relation with the canonical subriemannian contact structure $$\kappa = dt + 2(pdq - qdp)$$ . The main purpose is to give a complete description of the restriction to hypersurfaces of functions that belong to those Sobolev spaces, through a trace and lifting theorem. The function spaces of the restrictions involve an additional weight in the space variable, near points where the contact structure of ℍd agrees with the hypersurface.