On negative eigenvalues of two-dimensional Schroedinger operators with singular potentials

Abstract

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.

arXiv commentThis version contains minor corrections to the journal version. arXiv admin note: text overlap with arXiv:1609.08098

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Cited by in corpus (3)

• Weyl's laws and Connes' integration formulas for matrix-valued $L\log L$-Orlicz potentials
• Calogero type bounds in two dimensions
• Lieb-Thirring estimates for singular measures