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.