Journal of Lie Theory 29 (2019), No. 3, 801--809
Copyright Heldermann Verlag 2019
Maximal Hypoellipticity for Left-Invariant Differential Operators on Lie Groups
Tommaso Bruno
Dip. di Scienze Matematiche, Politecnico di Torino, 10129 Torino, Italy
tommaso.bruno@polito.it
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.
Keywords: Maximal hypoellipticity, Lie groups, Laplace operators.
MSC: 35H10, 35H20, 22E30
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