Generalized Volterra operators mapping between Banach spaces of analytic functions

Abstract

We characterize boundedness and compactness of the classical Volterra operator $$T_g :H_{v_{\alpha }}^{\infty } \rightarrow H^{\infty }$$ induced by a univalent function g for standard weights $$v_{\alpha }$$ with $$0 \le \alpha < 1$$ , partly answering an open problem posed by A. Anderson, M. Jovovic and W. Smith. We also study boundedness, compactness and weak compactness of the generalized Volterra operator $$T_g^{\varphi }$$ mapping between Banach spaces of analytic functions on the unit disc satisfying certain general conditions.