  Smith et al. recently 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, we give the
complete characterizations of the conditions for the boundedness and
compactness of Volterra type operators $T_g$ and their companion operators
$S_g$ between weighted Banach spaces of analytic functions, which essentially
generalize their works.
