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 L2 of Rumin’s Laplacians on the contact complex of the Heisenberg groups.
Maximal hypoellipticity for left-invariant differential operators on Lie groups
Bruno T.
2019-01-01
Abstract
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 L2 of Rumin’s Laplacians on the contact complex of the Heisenberg groups.
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