Maximal Hypoellipticity for Left-Invariant Differential Operators on Lie Groups

摘要

Given a maximal hypoelliptic differential operator of arbitrary order, we prove that its graph norm controls the Sobolev norm of the same order if the operator has left-invariant principal part and lower order terms with bounded coefficients. As an application, we obtain the essential self-adjointness on L-2 of Rumin's Laplacians on the contact complex of the Heisenberg groups.