Nuclear Volterra composition operators between Bloch and weighted type spaces

TL;DR

This paper provides a complete characterization of nuclear Volterra composition operators between weighted type spaces and Bloch spaces, based on the symbols and weights involved, extending previous understanding of these operators.

Contribution

It introduces new characterizations of nuclear Volterra composition operators between various weighted and Bloch spaces, including conditions on symbols and weights.

Findings

Characterization of nuclear Volterra composition operators between weighted type spaces.

Extension of results to little weighted type spaces and Bloch spaces.

Explicit conditions on symbols and weights for nuclearity.

Abstract

In this paper, we completely characterize nuclear Volterra composition operators $T^\phi_g : \mathcal H^\infty_\nu \longrightarrow \mathcal H^\infty_\mu$ and $S^\phi_g : \mathcal H^\infty_\nu \longrightarrow \mathcal H^\infty_\mu$ acting between weighted type spaces in terms of the symbols $g$ and $\phi$ of $T^\phi_g$ and $S^\phi_g$ and weights $\nu$ and $\mu$, when the weights $\nu$ and $\mu$ are normal weights in the sense of Shields and Williams. Moreover, nuclear Volterra composition operators acting between little weighted type spaces and Bloch spaces of order $\beta$ are also characterized.