| 多圆柱上从加权Bergman空间到Bloch型空间的加权复合算子 |
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| 引用本文： | 吴玮玮,徐辉明.多圆柱上从加权Bergman空间到Bloch型空间的加权复合算子[J].浙江师范大学学报(自然科学版),2014(2):151-157. |
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| 作者姓名： | 吴玮玮 徐辉明 |
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| 作者单位： | 浙江师范大学数理与信息工程学院,浙江金华321004 |
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| 基金项目： | 国家自然科学基金资助项目（11271124;11271332）;浙江省自然科学基金资助项目（Y6110053） |
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| 摘 要： | 设Dn是Cn中的单位多圆柱,φ(z)=(φ1(z),φ2(z),…,φn(z))是Dn的一个全纯自映射,ψ(z)是Dn上的全纯函数.研究了单位多圆柱上从加权Bergman空间到Bloch型空间的加权复合算子ψCφ;通过φ和ψ的函数特征,分别给出了单位多圆柱上从加权Bergman空间到Bloch型空间的加权复合算子ψCφ的有界性和紧性的充分必要条件.
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| 关 键 词： | 加权Bergman空间 Bloch型空间 加权复合算子 有界性 紧性 |
Weighted composition operators from weighted Bergman space to Bloch-type spaces on the polydisc |
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| WU Weiwei,XU Huiming.Weighted composition operators from weighted Bergman space to Bloch-type spaces on the polydisc[J].Journal of Zhejiang Normal University Natural Sciences,2014(2):151-157. |
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| Authors: | WU Weiwei XU Huiming |
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| Institution: | (College of Mathematics, Physics and Information Engineering, Zhefiang Normal University, Jinhua Zhejiang 321004, China) |
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| Abstract: | Let φ（z）=（φ1（z）,φ2（z）,…,φn（z））be a holomorphic self-map of Dn and ψ（z）a holomorphic function on Dn ,where Dn is the unit polydisc of Cn . It was investigated the weighted composition operator ψCφfrom weighted Bergman space to the Bloch-type spaces on the unit polydisc. In terms of the function property of φ and ψ,the sufficient and necessary conditions were given for the weighted composition operator ψCφ to be bounded and compact from weighted Bergman space to the Bloch-type spaces. |
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| Keywords: | weighted Bergman space Bloch-type spaces weighted composition operator boundedness compactness |
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