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

Abstract

We present upper estimates for the number of negative eigenvalues of two-dimensional Schrodinger operators with potentials generated by Ahlfors regular measures of arbitrary fractional dimension α ∈ (0, 2]. The estimates are given in terms of integrals of the potential with a logarithmic weight and of its L log L type Orlicz norms. In the case α = 1, our results are stronger than the known ones about Schrodinger operators with potentials supported by Lipschitz curves.