Extended Cesáro 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 Tg 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 Tg from generally weighted Bloch spaces (0<α<∞) to Zygmund space Z in the unit ball, and also present some necessary and sufficient conditions.