Exceptional sets for the derivatives of Blaschke products

TL;DR

This paper investigates the growth behavior of the logarithmic derivative of Blaschke products near the boundary of the unit disk, providing estimates that exclude certain exceptional sets.

Contribution

It introduces new growth estimates for the derivatives of Blaschke products, specifically addressing the behavior outside exceptional sets.

Findings

Growth estimates for $B'(z)/B(z)$ as $|z| o 1$

Identification of exceptional sets where estimates hold

Enhanced understanding of boundary behavior of Blaschke products

Abstract

We obtain growth estimates for the logarithmic derivative $B'(z)/B(z)$ of a Blaschke product as $|z| \to 1$ and $z$ avoids some exceptional sets.