# On the discrete spectrum of Schroedinger operators with Ahlfors regular potentials in a strip

## TL;DR

This paper provides quantitative upper bounds on the number of eigenvalues below the essential spectrum for Schroedinger operators with Ahlfors regular potentials in a strip, considering Robin and Dirichlet boundary conditions, using weighted norms.

## Contribution

It introduces new upper estimates for eigenvalues of Schroedinger operators with Ahlfors regular potentials, expressed via weighted L^1 and Orlicz norms, for different boundary conditions.

## Key findings

- Eigenvalue bounds depend on weighted L^1 norms of potentials.
- Orlicz norms provide alternative estimates.
- Results apply to operators with Robin and Dirichlet boundary conditions.

## Abstract

In this paper, quantitative upper estimates for the number of eigenvalues lying below the essential spectrum of Schroedinger operators with potentials generated by Ahlfors regular measures in a strip subject to two different types of boundary conditions (Robin and Dirichlet respectively) are presented. The estimates are presented in terms of weighted L^1 norms and Orlicz norms of the potential.