Generalized Volterra operators mapping between Banach spaces of analytic functions

Abstract

We characterize boundedness and compactness of the classical Volterra operator $T_g:H_{v_{\alpha }}^{\infty }\to H^{\infty }$ 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 $T_g^{\phi }$ mapping between Banach spaces of analytic functions on the unit disc satisfying certain general conditions.