A new criterion for the boundedness and the compactness of the generalized weighted composition operators from the Bloch space into the Zygmund space is given in this paper.
LetBnbe the unit ball ofCn,H(Bn)the space of all holomorphic functions inBn. Letu∈H(Bn)andαbe a holomorphic self-map ofBn. Forf∈H(Bn), the weigthed composition operatoruCαis defined by(uCαf)(z)=u(z)f(α(z)),z∈Bn.The boundedness and compactness of the weighted composition operator on some weighted spaces on the unit ball are studied in this paper.
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