| Reinhardt域上一类推广的Roper-Suffridge算子 |
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| 引用本文： | 刘浩,夏红川. Reinhardt域上一类推广的Roper-Suffridge算子[J]. 数学学报, 2016, 59(2): 253-266 |
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| 作者姓名： | 刘浩 夏红川 |
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| 作者单位： | 1.河南大学数学与统计学院 开封 470001;2.厦门大学数学科学学院 厦门 361005 |
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| 基金项目： | 国家自然科学基金资助项目(11271359, 11471098) |
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| 摘 要： | 研究一类推广的Roper-Suffridge算子F(z)=(f(z_1)+f′(z_1)∑_(k=2)~nakz_k~pk,f′(z)1)(~1/p2)z_2,…,f′(z_1)~(1/pn)z_n)′,证明该算子在复欧氏空间中的Reinhardt域Ω_(n,p2,%…,pn)={z=(z_1,…,z_n)∈C~n:|z_|~2+∑_(k=2)~n|zk|~(pk)1,Pk∈N~+,k=2,…,n}上分别保持α次的殆β型螺形性,α次的β型螺形性及强β型螺形性.
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| 关 键 词： | Roper-Suffridge算子 双全纯映照 Reinhardt域 |
The Generalized Roper-Suffridge Operator on Reinhardt Domains |
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| Hao LIU,Hong Chuan XIA. The Generalized Roper-Suffridge Operator on Reinhardt Domains[J]. Acta Mathematica Sinica, 2016, 59(2): 253-266 |
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| Authors: | Hao LIU Hong Chuan XIA |
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| Affiliation: | 1.Institute of Mathematics and Statistics, He'nan University, Kaifeng 470001, P. R. China;2.Institute of Mathematical Science, Xiamen University, Xiamen 361005, P. R. China |
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| Abstract: | We study the generalized Roper-Suffridge operator (F(z1)+f'(z1)Σk =2nakzkpk, f' (z1)1/(p2)z2, . . ., f' (z1)1/(pn)zn)', and prove that it can preserve the properties of almost spirallikeness of type β and order α, spirallikeness of type β and order α, and strongly spirallikeness of type β on the following Reinhardt domain in complex Euclidean space Ωn,p2,...,pn = {z = (z1, . . ., zn) ∈ Cn : |z1|2 +Σk=2n |zk|pk < 1, pk ∈ N+, k = 2, . . ., n} under some special conditions, respectively. |
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| Keywords: | Roper-Suffridge operator biholomorphic mappings Reinhardt domains |
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