The main results are conditions on g such that the Volterra type operator is bounded or compact on BMOA. We also point out certain information when Jg is considered as an operator on a general space X of analytic functions on the disc.
Sisakis, Aristomenis G. and Zhao, Ruhan, "A Volterra Type Operator on Spaces of Analytic Functions" (1999). Mathematics Faculty Publications. 7.
A. Siskakis and R. Zhao: A Volterra type operator on spaces of analytic functions, Contemporary Mathematics, 232(1999), 299--311.