Research Article Weighted Composition Operators from H to the Bloch Space on the Polydisc
نویسندگان
چکیده
Let Dn be the unit polydisc of Cn. The class of all holomorphic functions with domain Dn will be denoted by H(Dn). Let φ be a holomorphic self-map of Dn, the composition operator Cφ induced by φ is defined by (Cφ f )(z) = f (φ(z)) for z ∈Dn and f ∈H(Dn). If, in addition, ψ is a holomorphic function defined on Dn, the weighted composition operator ψCφ induced by ψ and φ is defined by ψCφ(z) = ψ(z) f (φ(z)) for z in Dn and f ∈H(Dn). A function f holomorphic in Dn is said to belong to the Bloch space (Dn) if
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