Nuclear Volterra composition operators between Bloch and weighted type spaces

Abstract

In this paper, we completely characterize nuclear Volterra composition operators $T_g^{\varphi }:{\mathcal{H}}_{\nu }^{\infty }⟶{\mathcal{H}}_{\mu }^{\infty }$ and $S_g^{\varphi }:{\mathcal{H}}_{\nu }^{\infty }⟶{\mathcal{H}}_{\mu }^{\infty }$ acting between weighted type spaces in terms of the symbols $g$ and $\varphi$ of $T_g^{\varphi }$ and $S_g^{\varphi }$ 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.