Volterra-composition operators on the weighted Bergman space with exponential type weights

TL;DR

This paper investigates the properties of Volterra-composition operators on weighted Bergman spaces with exponential weights, establishing conditions for their boundedness and compactness when mapping to Bloch type spaces.

Contribution

It provides necessary and sufficient conditions for the boundedness and compactness of Volterra-composition operators on these specialized function spaces.

Findings

Characterization of bounded Volterra-composition operators

Criteria for compactness of these operators

Conditions linking operator properties to function space parameters

Abstract

The properties of Volterra-composition operators on the weighted Bergman space with exponential type weights are investigated in this paper. We state some necessary and sufficient conditions that a Volterra-composition operator from the weighted Bergman space to Bloch type space ( or little Bloch type space ) must satisfy for the Volterra-composition operator to be bounded or compact.