INEQUALITIES AND BOUNDS FOR THE EIGENVALUES OF THE SUB-LAPLACIAN ON A STRICTLY PSEUDOCONVEX CR MANIFOLD

Abstract

Abstract. We establish inequalities for the eigenvalues of the sub-Laplace operator associated with a pseudo-Hermitian structure on a strictly pseudoconvex CR manifold. Our inequalities extend those obtained by Niu and Zhang [26] for the Dirichlet eigenvalues of the sub-Laplacian on a bounded domain in the Heisenberg group and are in the spirit of the well known Payne-Pólya-Weinberger and Yang universal inequalities. hal-00779283, version 1- 28 Jan 2013 1

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