# Spectral inequalities for a class of integral operators

## TL;DR

This paper establishes spectral inequalities for a class of integral operators, providing bounds that relate to the eigenvalue distribution of the Laplace operator with Dirichlet boundary conditions.

## Contribution

It extends previous results by deriving new inequalities for Riesz means and the eigenvalue counting function of certain self-adjoint compact integral operators.

## Key findings

- Derived inequalities for Riesz means of discrete spectra
- Established bounds for the eigenvalue counting function of Laplace operators
- Extended previous spectral inequality results

## Abstract

We obtain inequalities for the Riesz means for the discrete spectrum of a class of self-adjoint compact integral operators. Such bounds imply some inequalities for the counting function of the Dirichlet boundary problem for the Laplace operator. The paper is an extension of the results previously obtained in [5].