On a blaschke-type condition for subharmonic functions with two sets of singularities on the boundary

Abstract

Given two compact sets, E and F, on the unit circle, we study the class of subharmonic functions on the unit disk which can grow at the direction of E and F (sets of singularities) at different rate. The main result concerns the Blaschke-type condition for the Riesz measure of such functions. The optimal character of this condition is demonstrated.