Generalized Volterra operators mapping between Banach spaces of analytic functions

Abstract

We characterize boundedness and compactness of the classical Volterra operator $T_g \colon H_{v_α}^{\infty} \to H^{\infty}$ induced by a univalent function $g$ for standard weights $v_α$ with $0 \leq α< 1$, 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 $T_g^φ$ mapping between Banach spaces of analytic functions on the unit disc satisfying certain general conditions.