A proof of Hormander's theorem for sublaplacians on Carnot groups

摘要

We give a self-contained analytical proof of Hormander's hypoellipticity theorem in the case of left invariant sub-laplacians of Carnot groups. The proof does not rely on pseudodifferential calculus and provides intermediate regularity estimates expressed in terms of Sobolev spaces induced by right invariant vector fields. (C) 2015 Elsevier Ltd. All rights reserved.