# On negative eigenvalues of two-dimensional Schrödinger operators with singular potentials

@article{Karuhanga2019OnNE,
title={On negative eigenvalues of two-dimensional Schr{\"o}dinger operators with singular potentials},
author={Martin Karuhanga and Eugene Shargorodsky},
journal={arXiv: Spectral Theory},
year={2019}
}
• Published 10 December 2019
• Mathematics
• arXiv: Spectral Theory
We present upper estimates for the number of negative eigenvalues of two-dimensional Schroedinger operators with potentials generated by Ahlfors regular measures of arbitrary dimension $\alpha\in (0, 2]$.The estimates are given in terms of the integrals of the potential with a logarithmic weight and of its L $\log$ L type Orlicz norms. In the case $\alpha = 1$, our estimates are stronger than the known ones about Schroedinger operators with potentials supported by Lipschitz curves.
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