| COMPOSITION OPERATORS ON ANALYTIC VECTOR-VALUED NEVANLINNA CLASSES |
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| 作者姓名： | 王茂发 |
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| 作者单位： | [1]Wuhan Institute of Physics and Mathematics, CAS, Wuhan 430071, China [2]School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China |
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| 基金项目： | This research is supported by the NNSF of China （10401027;10271117;10371093）. |
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| 摘 要： | Let φ be an analytic self-map of the complex unit disk and X a Banach space. This paper studies the action of composition operator Cφ： f→foφ on the vector-valued Nevanlinna classes N（X） and Na（X）. Certain criteria for such operators to be weakly compact are given. As a consequence, this paper shows that the composition operator Cφ is weakly compact on N（X） and Na（X） if and only if it is weakly compact on the vector-valued Hardy space H^1 （X） and Bergman space B1（X） respectively.
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| 关 键 词： | 合成算子 界限值 弱紧密 Carleson测量 向量值 |
| 收稿时间： | 2004-10-23 |
COMPOSITION OPERATORS ON ANALYTIC VECTOR-VALUED NEVANLINNA CLASSES |
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| Wang Maofa.COMPOSITION OPERATORS ON ANALYTIC VECTOR-VALUED NEVANLINNA CLASSES[J].Acta Mathematica Scientia,2005,25(4):771-780. |
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| Authors: | Wang Maofa |
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| Institution: | 1. Wuhan Institute of Physics and Mathematics, CAS, Wuhan 430071, China;2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;1. Instituto Argentino de Matemática “Alberto P. Calderón”, Saavedra 15 3° piso, C1083ACA, Ciudad Autónoma de Buenos Aires, Argentina;2. Instituto de Ciencias, Universidad Nacional de General Sarmiento, J.M. Gutierrez 1150, B1613GSX, Los Polvorines, Pcia. de Buenos Aires, Argentina;1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China;2. Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China;1. Department of Mathematics, University at Albany, Albany, NY 12222, USA;2. Department of Mathematics, University of Reading, Reading RG6 6AX, UK;1. University of Florida, United States of America;2. University of Manitoba, Canada |
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| Abstract: | Let ψ be an analytic self-map of the complex unit disk and X a Banach space.This paper studies the action of composition operator Cψ: f → fo ψ on the vector-valued Nevanlinna classes N(X) and Na(X). Certain criteria for such operators to be weakly compact are given. As a consequence, this paper shows that the composition operator Cψ is weakly compact on N(X) and Na(X) if and only if it is weakly compact on the vector-valued Hardy space H1 (X) and Bergman space B1 (X) respectively. |
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| Keywords: | Composition operator boundedness weak compactness Carleson measure vector-valued Nevanlinna class |
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