Abstract
Here we introduce thenth weighted space on the upper half-planeΠ+={z∈ℂ:Im z>0}in the complex planeℂ. For the casen=2, we call it the Zygmund-type space, and denote it by𝒵(Π+). The main result of the paper gives some necessary and sufficient conditions for the boundedness of the composition operatorCφf(z)=f(φ(z))from the Hardy spaceHp(Π+)on the upper half-plane, to the Zygmund-type space, whereφis an analytic self-map of the upper half-plane.
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