Generalized Volterra operators mapping between Banach spaces of analytic functions

We characterize boundedness and compactness of the classical Volterra operator $T_g\text{\hspace{0.17em}⁣}:H_{v_{\alpha }}^{\mathrm{\infty }}\to H^{\mathrm{\infty }}$ induced by a univalent function $g$ for standard weights $v_{\alpha }$ with $0 \leq \alpha < 1$, 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 $T_g^{\phi }$ mapping between Banach spaces of analytic functions on the unit disc satisfying certain general conditions.