Generalized composition operators and Volterra composition operators on Bloch spaces in the unit ball

Let H( B) denote the space of all holomorphic functions on the unit ball B of C-n. Let phi=(phi(1), ... ,phi(n)) be a holomorphic self-map of B and g is an element of H(B). In this article, we consider the following generalized composition operator: C(phi)(g)f(z) = integral(1)(0) Rf(phi(tz))g(tz)dt/t, f is an element of H(B), g(0) =0, and the following Volterra composition operator: V(phi)(g)f(z) = integral(1)(0) f(phi(tz))Rg(tz)dt/t, f is an element of H(B). The boundedness and compactness of the operators C-phi(g) and V-phi(g) on Bloch spaces in the unit ball are studied.