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In this paper, we derive "universal" inequalities for the sums of eigenvaluesof the Hodge de Rham Laplacian on Euclidean closed Submanifolds and ofeigenvalues of the Kohn Laplacian on the Heisenberg group. These inequalitiesgeneralize the Levitin-Parnovski inequality obtained for the sums ofeigenvalues of the Dirichlet Laplacian of a bounded Euclidean domain. NewReilly and Asada inequalities are also obtained.

A Generalization of a Levitin and Parnovski Universal Inequality for Eigenvalues