Authors: | Stević, Stevo | Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Title: | Composition operators from the hardy space to the zygmund-type space on the upper half-plane | Journal: | Abstract and Applied Analysis | Volume: | 2009 | Issue Date: | 21-May-2009 | Rank: | M21a | ISSN: | 1085-3375 | DOI: | 10.1155/2009/161528 | Abstract: | Here we introduce the nth weighted space on the upper half-plane Π + ={ z∈ℂ:Im z∈ >0 } in the complex plane ℂ. For the case n=2, we call it the Zygmund-type space, and denote it by script Z sign(Π +). The main result of the paper gives some necessary and sufficient conditions for the boundedness of the composition operator C φ f(z)=f(φ(z)) from the Hardy space H p (Π +) on the upper half-plane, to the Zygmund-type space, where φ is an analytic self-map of the upper half-plane. |
Publisher: | Hindawi |
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