| 刘小松.多复变数某类推广的螺型映射精确的系数估计[J].数学年刊A辑,2024,(1):109~122 |
| 多复变数某类推广的螺型映射精确的系数估计 |
| The Sharp Coefficient Estimates for a Certain General Class of Spirallike Mappings in Several Complex Variables |
| Received:January 27, 2022 Revised:November 11, 2022 |
| DOI：10.16205/j.cnki.cama.2024.0008 |
| 中文关键词: β型螺形映射 主要系数 齐次展开式 精细的系数估计 k折对称 |
| 英文关键词:Spirallike mapping of type β Main coefficient Homogeneous expansion Refined coefficient estimate k-Fold symmetric |
| 基金项目:国家自然科学基金(No.11871257,No.12071130) |
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| 中文摘要: |
| 主要用统一方法建立限制条件下复Banach空间单位球与Cn中单位多圆柱上某类推广的β型螺型映射全部项齐次展开式的精细估计.同时,也用统一方法建立较弱限制条件下Cn中Dp1,p2,…,pn=■,pl>1,l=1,2,…,n上某类推广的β型螺型映射主要系数的精细估计.特别地,限制条件下k折对称β型螺型映射的结果是精确的.所得结果包含前面文献中许多已知结论. |
| 英文摘要: |
| In this article, the author chiefly establishes the refined estimates of all homogeneous expansions for a
certain general class of spirallike mappings of type $\beta$ on the unit ball in complex Banach spaces and the unit
polydisk in $\mathbb{C}^n$ under restricted conditions with a unified method. Meanwhile, the author obtains the refined estimates
of main coefficient for a certain general class of spirallike mappings of type $\beta$ on
$D_{p_1,p_2,\cdots,p_n}=\big\{z\in \mathbb{C}^n: \sum\limits_{l=1}^n|z_l|^{p_l}<1\big\}, p_l>1, l=1,2,\cdots,n$
on $\mathbb{C}^n$ under weaker restricted conditions with a unified method as well. In particular,
the results are sharp for $k$-fold symmetric spirallike mapping of type $\beta$ under additional assumptions.
The derived results include many known results in the prior references. |
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