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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| Format: | Article |
| Language: | English |
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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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| author | Stevo Stević |
| author_facet | Stevo Stević |
| author_sort | Stevo Stević |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-71657eb1b66f4dc1a5f707814ca2f39f |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-71657eb1b66f4dc1a5f707814ca2f39f2025-02-03T07:25:57ZengWileyAbstract and Applied Analysis1085-33751687-04092009-01-01200910.1155/2009/161528161528Composition Operators from the Hardy Space to the Zygmund-Type Space on the Upper Half-PlaneStevo Stević0Mathematical Institute of the Serbian Academy of Sciences, Knez Mihailova 36/III, 11001 Beograd, SerbiaHere 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.http://dx.doi.org/10.1155/2009/161528 |
| spellingShingle | Stevo Stević Composition Operators from the Hardy Space to the Zygmund-Type Space on the Upper Half-Plane Abstract and Applied Analysis |
| title | Composition Operators from the Hardy Space to the Zygmund-Type Space on the Upper Half-Plane |
| title_full | Composition Operators from the Hardy Space to the Zygmund-Type Space on the Upper Half-Plane |
| title_fullStr | Composition Operators from the Hardy Space to the Zygmund-Type Space on the Upper Half-Plane |
| title_full_unstemmed | Composition Operators from the Hardy Space to the Zygmund-Type Space on the Upper Half-Plane |
| title_short | Composition Operators from the Hardy Space to the Zygmund-Type Space on the Upper Half-Plane |
| title_sort | composition operators from the hardy space to the zygmund type space on the upper half plane |
| url | http://dx.doi.org/10.1155/2009/161528 |
| work_keys_str_mv | AT stevostevic compositionoperatorsfromthehardyspacetothezygmundtypespaceontheupperhalfplane |