Integration and differentiation operators between growth spaces

TL;DR

This paper investigates the properties of integration and differentiation operators between various growth spaces of analytic functions, focusing on the role of log-convex weights on the complex plane and unit disk.

Contribution

It provides new characterizations of these operators' boundedness and compactness for general radial weights, emphasizing the significance of log-convex weights.

Findings

Characterization of the integration operator between growth spaces

Analysis of the differentiation operator on Hardy growth spaces

Identification of the special role of log-convex weights

Abstract

For arbitrary radial weights $w$ and $u$, we study the integration operator between the growth spaces $H_w^\infty$ and $H_u^\infty$ on the complex plane. Also, we investigate the differentiation operator on the Hardy growth spaces $H_w^p$, $0<p<\infty$, defined on the unit disk or on the complex plane. As in the case $p=\infty$, the log-convex weights $w$ play a special role in the problems under consideration.