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, 1-8

Abstract:

Here we introduce the ð ‘› th weighted space on the upper half-plane Î + = { 𠑧 ∈ â„‚ ∶ I m 𠑧 > 0 } in the complex plane â„‚ . For the case ð ‘› = 2 , we call it the Zygmund-type space, and denote it by ð ’µ ( Î + ) . The main result of the paper gives some necessary and sufficient conditions for the boundedness of the composition operator ð ¶ ð œ‘ ð ‘“ ( 𠑧 ) = ð ‘“ ( 𠜑 ( 𠑧 ) ) from the Hardy space ð » ð ‘ ( Î + ) on the upper half-plane, to the Zygmund-type space, where 𠜑 is an analytic self-map of the upper half-plane.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:161528

DOI: 10.1155/2009/161528

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