| 刘小松.多复变数某些双全纯映射子族精确的系数估计[J].数学年刊A辑,2021,42(1):23~32 |
| 多复变数某些双全纯映射子族精确的系数估计 |
| The Sharp Coefficient Estimates for Some Subclasses of Biholomorphic Mappings in Several Complex Variables |
| Received:March 17, 2020 Revised:November 20, 2020 |
| DOI：10.16205/j.cnki.cama.2021.0003 |
| 中文关键词: 双全纯映射, 齐次展开式, 主要系数估计, Fekete-Szeg不等式 |
| 英文关键词:Biholomorphic mapping, Homogeneous expansion, Main coefficient estimate, Fekete-Szeg¨o inequality |
| 基金项目:国家自然科学基金 (No.,11871257) |
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| 中文摘要: |
| 作者建立了复Banach空间单位球上和mathbb{C}^n 中单位多圆柱上限制条件下双全纯映射齐次展开式的精确估计和Fekete-Szeg"{o}不等式,同时给出mathbb{C}^n 中D_{p_1,p_2,cdots,p_n}=big{zin mathbb{C}^n: sumlimits_{l=1}^n|z_l|^{p_l}<1big} ( p_l>1, l=1,2,cdots,n)上限制条件下双全纯映射主要系数的精确估计和Fekete-Szeg"{o}不等式.所得结果推广了单复变几何函数论中相应的经典结论. |
| 英文摘要: |
| In this paper, the sharp estimates of all homogeneous expansions and the FeketeSzeg¨o inequality for biholomorphic mappings defined on the unit ball of complex Banach spaces and the unit polydisk in Cn are established with some restricted condition. Meanwhile, the sharp main coefficient estimates and the Fekete-Szeg¨o inequality for biholomorphic mappings on Dp1,p2,··· ,pn =z ∈ Cn : nlP=1 |zl|pl < 1 |
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