Volterra type operators on weighted Banach spaces of analytic functions

TL;DR

This paper provides complete characterizations of when Volterra type operators and their companions are bounded and compact on weighted Banach spaces of analytic functions, generalizing previous results.

Contribution

It extends prior work by offering full criteria for boundedness and compactness of Volterra operators on weighted spaces, including companion operators.

Findings

Characterization of boundedness conditions for $T_g$ and $S_g$

Criteria for compactness of Volterra type operators

Generalization of previous boundedness results

Abstract

Smith et al. recently gave the sufficient and necessary conditions for the boundedness of Volterra type operators on Banach spaces of bounded analytic functions when the symbol functions are univalent. In this paper, we give the complete characterizations of the conditions for the boundedness and compactness of Volterra type operators $T_g$ and their companion operators $S_g$ between weighted Banach spaces of analytic functions, which essentially generalize their works.