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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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′‖∞. |
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| ISSN: | 0972-6802 |