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

The paper defines an extended Cesaro operator T-g with holomorphic symbol g in the unit ball B of C-n as T-g(f)(z)=integral(0)(1)f(tz)Rg(tz)dt/t, fis an element ofH(B),zis an element ofB. Where Rg(z) = Sigma(j=1)(n) z(j) partial derivativeg/partial derivativez(j) is the radial derivative of g. In this paper, the author characterizes g for which T-g is bounded (or compact) on the Bloch space B and the little Bloch space B-0.