Composition operators from ℬα to QK type spaces
Suppose that ϕ is an analytic self-map of the unit disk Δ. Necessary and sufficient condition are given for the composition operator Cϕf=fοϕ to be bounded and compact from α-Bloch spaces to QK type spaces which are defined by a nonnegative, nondecreasing function k(r) for 0≤r<∞. Moreover, the com...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2008/383496 |
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| _version_ | 1832550649267486720 |
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| author | Jizhen Zhou |
| author_facet | Jizhen Zhou |
| author_sort | Jizhen Zhou |
| collection | DOAJ |
| description | Suppose that ϕ is an analytic self-map of the unit disk Δ. Necessary and sufficient condition are given for the composition operator Cϕf=fοϕ to be bounded and compact from α-Bloch spaces to QK type spaces which are defined by a nonnegative, nondecreasing function k(r) for 0≤r<∞. Moreover, the compactness of composition operator Cϕ from ℬ0 to QK type spaces are studied, where ℬ0 is the space of analytic functions of f with f′∈H∞ and ‖f‖ℬ0=|f(0)|+‖f′‖∞. |
| format | Article |
| id | doaj-art-a9106c9f6de845e683cfa3417a958e7b |
| institution | Kabale University |
| issn | 0972-6802 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-a9106c9f6de845e683cfa3417a958e7b2025-02-03T06:06:12ZengWileyJournal of Function Spaces and Applications0972-68022008-01-01618810410.1155/2008/383496Composition operators from ℬα to QK type spacesJizhen Zhou0Department of Mathematics and Physics, Anhui University of Science and Technology, Anhui, Huainan 232001, ChinaSuppose that ϕ is an analytic self-map of the unit disk Δ. Necessary and sufficient condition are given for the composition operator Cϕf=fοϕ to be bounded and compact from α-Bloch spaces to QK type spaces which are defined by a nonnegative, nondecreasing function k(r) for 0≤r<∞. Moreover, the compactness of composition operator Cϕ from ℬ0 to QK type spaces are studied, where ℬ0 is the space of analytic functions of f with f′∈H∞ and ‖f‖ℬ0=|f(0)|+‖f′‖∞.http://dx.doi.org/10.1155/2008/383496 |
| spellingShingle | Jizhen Zhou Composition operators from ℬα to QK type spaces Journal of Function Spaces and Applications |
| title | Composition operators from ℬα to QK type spaces |
| title_full | Composition operators from ℬα to QK type spaces |
| title_fullStr | Composition operators from ℬα to QK type spaces |
| title_full_unstemmed | Composition operators from ℬα to QK type spaces |
| title_short | Composition operators from ℬα to QK type spaces |
| title_sort | composition operators from bα to qk type spaces |
| url | http://dx.doi.org/10.1155/2008/383496 |
| work_keys_str_mv | AT jizhenzhou compositionoperatorsfrombatoqktypespaces |