Integral means of the derivatives of Blaschke products

TL;DR

This paper investigates the growth rates of integral means of derivatives of Blaschke products and functions in associated model subspaces, extending classical results in complex analysis.

Contribution

It generalizes classical results on growth rates of derivatives of Blaschke products and analyzes integral means in model subspaces.

Findings

Derived new growth rate estimates for derivatives of Blaschke products.

Extended classical results to functions in model subspaces.

Provided explicit growth rates for integral means of derivatives.

Abstract

We study the rate of growth of some integral means of the derivatives of a Blaschke product and we generalize several classical results. Moreover, we obtain the rate of growth of integral means of the derivative of functions in the model subspace $K_B$ generated by the Blaschke product $B$