Melas-type bounds for the Heisenberg Laplacian on bounded domains

TL;DR

This paper derives refined bounds for the eigenvalues of the Heisenberg Laplacian on bounded domains, improving previous results by including sharp leading and lower order terms.

Contribution

It introduces new inequalities for Riesz means of eigenvalues, enhancing the understanding of spectral properties of the Heisenberg Laplacian.

Findings

Established a sharp leading term in eigenvalue bounds.

Included a lower order correction term in the bounds.

Improved upon previous results by Hanson and Laptev.

Abstract

We study Riesz means of the eigenvalues of the Heisenberg Laplacian with Dirichlet boundary conditions on bounded domains. We obtain an inequality with a sharp leading term and an additional lower order term, improving the result of Hanson and Laptev.