Extended Cesaro operators on the Bloch space in the unit ball of CN

We define an extended Cesaro operator T-g with holomorphic symbol g in the unit ball B of C-n as 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 Rg(z) = Sigma(n)(j=1) a(j)partial derivative g/partial derivative z(j) is the radial derivative of g. In this paper we characterize those g for which T-g is bounded (or compact) on the Bloch space B and the little Bloch space B-0.