A note about Volterra operators on weighted Banach spaces of entire functions

TL;DR

This paper characterizes the boundedness, compactness, and weak compactness of Volterra operators between weighted Banach spaces of entire functions, extending previous results to new function spaces.

Contribution

It provides a comprehensive characterization of Volterra operators on weighted Banach spaces of entire functions, complementing existing work on related function spaces.

Findings

Characterization of boundedness, compactness, and weak compactness of Volterra operators

Extension of previous results to new weighted Banach spaces of entire functions

Conditions expressed in terms of the symbol g

Abstract

We characterize boundedness, compactness and weak compactness of Volterra operators acting between different weighted Banach spaces of entire functions with weighted sup-norms in terms of the symbol g. Thus we complement recent work by Bassallote, Contreras, Hern\'andez-Mancera, Mart\'in and Paul for spaces of holomorphic functions on the disc and by Constantin and Pel\'aez for reflexive weighted Fock spaces.