| 王安,孙立岩,刘颖.Schwarz引理与Schwarz-Pick引理在单位球B_n上的推广[J].数学年刊A辑,2011,32(5):579~592 |
| Schwarz引理与Schwarz-Pick引理在单位球B_n上的推广 |
| Generalization of Schwarz Lemma and Schwarz-Pick Lemma on the Unit Ball B_n |
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| DOI： |
| 中文关键词: Schwarz引理 Schwarz-Pick引理 全纯自同构变换 |
| 英文关键词:Schwarz lemma Schwarz-Pick lemma Holomorphic automorphism transformation |
| 基金项目:国家自然科学基金(No.11071171); 北京自然科学基金(No.1082005)资助的项目 |
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| 中文摘要: |
| 对单复变中的Schwarz引理与Schwarz-Pick引理在$\mathbb{C}^{n}$中的超球上进行
了推广. 考虑$\mathbb{C}^{n}$中单位球$ B_{n}$上模小于1的全纯函数 $f(z)$, 并在$f(0)=0$的条件下
给出函数在原点的任意阶导数的估计. 更进一步地, 得到了$ B_{n}$上模小于1的任意
全纯函数在任意点的高阶导数的估计. |
| 英文摘要: |
| The Schwarz lemma and the Schwarz-Pick lemma are generalized on the unit ball $ B_{n}$ in $\mathbb{C}^{n}$.
Considering the holomorphic function $f(z)$ whose norm is less than 1 on the unit ball $ B_{n}$ in
$\mathbb{C}^{n}$, when
$f(0)=0$, the authors get the estimate of any order derivatives of $f(z)$ at the origin. In addition,
the authors obtain an estimate for higher order derivatives of a holomorphic function which norm is less than 1 of
$B_{n}$. |
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