Derivatives of Blaschke Products and Model Space Functions

TL;DR

This paper explores how the zero distribution of Blaschke products influences the inclusion of their derivatives and model space functions in weighted Bergman spaces, revealing new connections in complex analysis.

Contribution

It provides new insights into the relationship between zero distribution of Blaschke products and the function space properties of their derivatives and model spaces.

Findings

Characterizes conditions for derivatives of Blaschke products to belong to weighted Bergman spaces.

Establishes links between zero distribution and model space function behavior.

Provides criteria for inclusion based on zero distribution patterns.

Abstract

The relationship between the distribution of zeros of an infinite Blaschke product $B$ and the inclusion in weighted Bergman spaces $A_{\alpha}^p$ of the derivative of $B$ or the derivative of functions in its model space $H^2 \ominus BH^2$ is investigated.