Trace and trace lifting theorems in weighted Sobolev spaces. (English) Zbl 1089.35016

Bahouri, Hajer; Chemin, Jean-Yves; Xu, Chao-Jiang

J. Inst. Math. Jussieu 4, No. 4, 509-552 (2005).

Summary: We prove in this work the trace and trace lifting theorems for the Sobolev spaces associated with a system of Hörmander’s vectors fields of order 2. The case of nondegenerate characteristic points for left invariant vector fields on the Heisenberg group is also studied.

MSC:

35H10	Hypoelliptic equations
46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
47G30	Pseudodifferential operators

Keywords:

trace and trace lifting; Heisenberg group; Hörmander condition; Weyl-Hörmander calculus