Estimates of Green potentials. Applications

Optimal Cartan-type covers by hyperbolic discs of carriers of Green $\alpha$-potentials are obtained in a simply connected domain in the complex plane and estimates of the potentials outside the carriers are presented. These results are applied to problems on the separation of singularities of analytic and harmonic functions. For instance, uniform and integral estimates in terms of Green capacities of components of meromorphic functions are obtained.