| 多复变数一类α次星形映射齐次展开式各项的精细估计 |
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| 引用本文： | 刘小松,刘太顺. 多复变数一类α次星形映射齐次展开式各项的精细估计[J]. 数学学报, 2018, 61(6): 1029-1036 |
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| 作者姓名： | 刘小松 刘太顺 |
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| 作者单位： | 1. 岭南师范学院数学与统计学院 湛江 524048;2. 湖州师范学院数学系 湖州 313000 |
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| 基金项目： | 国家自然科学基金资助项目（11471111）；广东省自然科学基金资助项目（2014A030307016） |
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| 摘 要： | 本文首先给出复Banach空间单位球上一类α次星形映射齐次展开式各项的精细估计,特别当这些映射又是k折对称映射时,估计还是精确的.其次建立C~n中单位多圆柱上上述推广映射齐次展开式各项的精细估计,同样当这些映射又是k折对称映射时,估计仍是精确的.由此证明了多复变数中关于α次星形映射的弱Bieberbach猜想,且所得到的估计都能回到单复变数的情形.
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The Refined Estimates of All Homogeneous Expansions for a Subclass of Starlike Mappings of Order α in Several Complex Variables |
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| Xiao Song LIU,Tai Shun LIU. The Refined Estimates of All Homogeneous Expansions for a Subclass of Starlike Mappings of Order α in Several Complex Variables[J]. Acta Mathematica Sinica, 2018, 61(6): 1029-1036 |
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| Authors: | Xiao Song LIU Tai Shun LIU |
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| Affiliation: | 1. School of Mathematics and Computation Science, Lingnan Normal University, Zhanjiang 524048, P. R. China;2. Department of Mathematics, Huzhou Teachers College, Huzhou 313000, P. R. China |
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| Abstract: | We first obtain the refined estimates of all homogeneous expansions for a subclass of starlike mappings of order α on the unit ball in complex Banach spaces, especially the estimates are all sharp if these mappings are k-fold symmetric mappings. We next establish the refined estimates of all homogeneous expansions for the above generalized mappings on the unit polydisk in Cn. In particular, the estimates are also all sharp if these mappings are k-fold symmetric mappings. It is shown that we have proved a weak version of the Bieberbach conjecture for starlike mappings of order α in the case of several complex variables, and the derived results reduce to the classical results in the case of one complex variable. |
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| Keywords: | homogeneous expansion a zero of order k+1 k-fold symmetric mapping starlike mapping of order α Bieberbach conjecture |
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