In this paper, we are concerned with the Riesz means of Dirichlet eigenvalues for the sub-Laplace operator on the Engel group and deriver different inequalities for Riesz means. The Weyl-type estimates for means of eigenvalues are given.
Let X j , Y j (j = 1, • • •, n) be vector fields satisfying Hörmander's condition andIn this paper, we establish some inequalities of Dirichlet eigenvalues for degenerate elliptic partial differential operator ∆ L and ∆ 2 L . These inequalities extend Yang's inequalities for Dirichlet eigenvalues of Laplacian to the settings here and the forms of inequalities are more general than Yang's inequalities. To obtain them, we give a generalization of the inequality by Chebyshev.
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