Differentiation and integration operators on weighted Banach spaces of holomorphic functions

TL;DR

This paper investigates the boundedness of differentiation and integration operators on weighted Banach spaces of holomorphic functions, revealing limitations of previous results and introducing a new, more general approach with characterizations of radial weights.

Contribution

It introduces a novel elementary method to analyze operator boundedness on weighted spaces, extending applicability to general weights and domains, and provides new characterizations of radial weights.

Findings

Previous results may fail without additional conditions

A new elementary approach is developed for general weights and domains

Characterizations of popular classes of radial weights are established

Abstract

We show that some previous results concerning the boundedness of differentiation and integration operators on weighted spaces given by radial weights in the unit disk or the complex plane might fail without some natural additional conditions. In view of this we develop a new elementary approach which is essentially different from the previous one and can be applied for weights and domains of general types. We also establish a new characterization of some popular classes of radial weights.