On an integral operator on the unit ball in Cn

Let H(B) denote the space of all holomorphic functions on the unit ball B subset of C-n. In this paper, we investigate the integral operator T-g(f)(z) = integral(1)(0) f(tz)Rg(tz)(dt/t), f is an element of H(B), z is an element of B, where g is an element of H(B) and Rg(z) = Sigma(n)(j=1)z(j)(partial derivative g/partial derivative z(j))(z) is the radial derivative of g. The operator can be considered as an extension of the Cesaro operator on the unit disk. The boundedness of the operator on a-Bloch spaces is considered.