Generalized weighted composition operators from Zygmund spaces to Bloch–Orlicz type spaces

Let DD be the open unit disk in the complex plane CC and H(D)H(D) the class of all analytic functions on DD. Let φ be an analytic self-map of DD and ψ∈H(D)ψ∈H(D). In this paper the boundedness and compactness of the generalized weighted composition operator Dφ,ψnf=ψf(n)∘φ from the Zygmund space to the Bloch–Orlicz space and the little Bloch–Orlicz space are characterized.