On Blaschke products with derivatives in Bergman spaces with normal weights

TL;DR

This paper extends conditions for interpolating sequences and membership of derivatives in Bergman spaces with normal weights, providing new insights into Blaschke products and inner functions.

Contribution

It generalizes known conditions to broader Bergman spaces with normal weights and introduces new results on derivatives and interpolating Blaschke products.

Findings

Extended sufficient conditions for interpolating sequences

Established membership criteria for derivatives of Blaschke products

Applied duality techniques to derive new results

Abstract

We generalize a well-known sufficient condition for interpolating sequences for the Hilbert Bergman spaces to other Bergman spaces with normal weights (as defined by Shields and Williams) and obtain new results regarding the membership of the derivative of a Blashke product or a general inner function in such spaces. We also apply duality techniques to obtain further results of this type and obtain new results about interpolating Blaschke products.