| 多圆盘上Hardy空间之间复合算子列的总体紧性 |
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| 引用本文： | 江治杰,柏宏彬.多圆盘上Hardy空间之间复合算子列的总体紧性[J].四川理工学院学报(自然科学版),2007,20(5):70-73. |
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| 作者姓名： | 江治杰 柏宏彬 |
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| 作者单位： | 四川理工学院数学系,四川,自贡,643000 |
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| 摘 要： | 设φ:Dm→D为全纯映射,对ξ=(ξ1,ξ2,…ξm)∈Tm,文章利用切片函φξ:D→D,φξ(z)=φ(zξ)定义的计数函数Nφ(z)=∫TmNξ(z)dσ(ξ)研究复合算子列Cφn:H2(D)→H2(Dm)n的总体紧性。得到了如下定理:设φn:Dm→D为全纯映射列,Cφn:H2(D)→H2(Dm)为一致有界复合算子列,则η∞({n})=0当且仅当lim n→∞∣z∣→-Nφn(z)-log∣z∣=0。
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| 关 键 词： | 总体紧算子列 复合算子 Nevanlinna计数函数 切片函数 |
| 文章编号： | 1673-1549（2007）05-0070-04 |
| 收稿时间： | 2007-10-09 |
Collective Compactness of Composition Operator Sequences Between Hardy Spaces in Polydiscs |
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| JIANG Zhi-jie,BAI Hong-bin.Collective Compactness of Composition Operator Sequences Between Hardy Spaces in Polydiscs[J].Journal of Sichuan University of Science & Engineering:Natural Science Editton,2007,20(5):70-73. |
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| Authors: | JIANG Zhi-jie BAI Hong-bin |
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| Abstract: | Suppose φn:Dm→Dis a holomorphic mapping sequence,we characterize the collective compactness of composition operator sequence Cφn:H2(D)→H2(Dm) by counting functionNφn,which is defined as Nφ(z)=∫TmNξ(z)dσ(ξ),where φn,ξ is Slice function φn,ξ(z) = φn(zξ) for ξ =(1,ξ2,…,ξn),z ∈ D.Concretely,we obtain the follwing theorem: Suppose φn : D m→Dis a holomorphic mapping sequence and Cφn:H2(D)→H2(Dm) is an uniformly bouned composition operator sequence,thenη∞({n})=0 if and only if lim n→∞∣z∣→-Nφn(z)-log∣z∣=0。 |
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| Keywords: | collectively compact composition operator sequence composition operator Nevalinna counting function slice function |
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