Extended Cesلro operators from generally weighted Bloch spaces to Zygmund space

Let g be a holomorphic function of the unit ball B in the n-dimensional complex space, and denote by T g the extended Cesáro operator with symbol g. Starting with a brief introduction to well-known results about Cesáro operator, we investigate the boundedness and compactness of T g from generally weighted Bloch spaces B log α ( 0 < α < ∞ ) to Zygmund space Z in the unit ball, and also present some necessary and sufficient conditions.