Volterra Type Operators Between Bloch Type Spaces and Weighted Banach Spaces

Abstract

When the weight $\mu$ is more general than normal, the complete characterizations in terms of the symbol $g$ and weights for the conditions of the boundedness and compactness of $T_g: H^{\infty}_\nu\rightarrow H^{\infty}_\mu$ and $S_g: H^{\infty}_\nu\rightarrow H^{\infty}_\mu$ are still unknown. Smith et al. firstly 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, continuing their lines of investigations, we give the complete characterizations of the conditions for the boundedness and compactness of Volterra type operators $T_g$ and $S_g$ between Bloch type spaces $\mathcal{B}^\infty_\nu$ and weighted Banach spaces $H^{\infty}_\nu$ with more general weights, which generalize their works.