Composition Operators from the Hardy Space to the Zygmund‐Type Space on the Upper Half‐Plane

Stevo Stević

Abstract and Applied Analysis, 2009, vol. 2009, issue 1

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 𝒵(Π+). The main result of the paper gives some necessary and sufficient conditions for the boundedness of the composition operator Cφf(z) = f(φ(z)) from the Hardy space Hp(Π+) on the upper half‐plane, to the Zygmund‐type space, where φ is an analytic self‐map of the upper half‐plane.

Date: 2009
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https://doi.org/10.1155/2009/161528

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2009:y:2009:i:1:n:161528

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