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

## TL;DR

This paper investigates a Blaschke-type condition for subharmonic functions with singularities on two boundary sets, establishing optimal growth conditions and analyzing the Riesz measure in the unit disk.

## Contribution

It introduces a new Blaschke-type condition for subharmonic functions with boundary singularities on two sets, demonstrating its optimality.

## Key findings

- Established a Blaschke-type condition for the Riesz measure.
- Proved the optimality of the condition.
- Analyzed growth behavior of subharmonic functions near boundary singularities.

## 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 such condition is demonstrated.