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
投稿时间:2022-01-27  修订日期:2022-11-11
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)
作者单位
刘小松 岭南师范学院数学与统计学院, 广东 湛江 524048. 
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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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