Product-type operators on a class of Banach spaces of analytic functions into μ-Bloch spaces on the unit ball in Cn

Let B be an open unit ball in C-n. Let H(B) be the collection of all analytic functions on B and S(B) be the collection of all analytic self-maps on B. In this paper, we study the boundedness and compactness of the operator T-psi 0,T-psi 1,T-psi 2,T-phi f(z) = psi(0)(z)f(phi(z)) + psi(1)(z)Rf(phi(z)) + psi(2)(z)R(f circle phi)(z), where psi(0), psi(1), psi(2) is an element of H(B), phi is an element of S(B) and Rf denotes the radial derivative of f is an element of H(B), from a class of Banach spaces of analytic functions to mu-Bloch spaces on B and obtain estimates for its norm.