On critical points of Blaschke products

TL;DR

This paper establishes an upper bound for the derivative of Blaschke products with zeros in specific regions, linking critical points to a new analytic function space and deriving a Blaschke-type condition.

Contribution

It introduces a novel upper bound for derivatives of Blaschke products with zeros in Stolz-type regions and connects critical points to a recently defined analytic function space.

Findings

Derived an upper bound for derivatives of Blaschke products

Established a Blaschke-type condition for critical points

Linked critical points to a new analytic function space

Abstract

We obtain an upper bound for the derivative of a Blaschke product, whose zeros lie in a certain Stolz-type region. We show that the derivative belongs to the space of analytic functions in the unit disk, introduced recently in \cite{FG}. As an outcome, we obtain a Blaschke-type condition for critical points of such Blaschke products.