UNIVERSAL INEQUALITIES FOR EIGENVALUES OF QUADRATIC POLYNOMIAL OPERATOR OF THE KOHN LAPLACIAN

摘要

In this paper, we investigate the Dirichlet weighted eigenvalue problem of quadratic polynomial operator of the Kohn Laplacian on a bounded domain in the Heisenberg group H~n. We establish two inequalities for eigenvalues of this problem. One of them implies an explicit estimate for the upper bound of the (k+ l)-th eigenvalue in terms of the first k eigenvalues. Moreover, as a special case, we give some universal inequalities and estimates for eigenvalues of the bi-Kohn Laplacian.