Composition Operators from the Hardy Space to the Zygmund-Type Space on the Upper Half-Plane
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 th...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2009/161528 |
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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |