The trace problem for Sobolev spaces over the Heisenberg group
Let \(\mathbb H^d\) be the Heisenberg group. It can be identified with \({\mathbb R}^{2d+1}\) by the exponential coordinates \(x=(p,q,t)\), \(p,q\in {\mathbb R}^d\), \(t\in {\mathbb R}\). The author studies the trace problem for microlocally weighted Hilbertian Sobolev spaces over the Heisenberg group \(\mathbb H^d\) in relation with the canonical sub-Riemannian contact structure \(\varkappa= dt+2(p\, dq- q\, dp)\). The main result of the paper is 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 \(\mathbb H^d\) agrees with the hypersurface.
scientific article; zbMATH DE number 5279123
scientific article