| Schwarz引理与Schwarz-Pick引理在单位球B_n上的推广 |
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| 引用本文： | 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(中文版), 2011, 32(5): 579-592 |
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| 作者姓名： | 王安 孙立岩 刘颖 |
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| 作者单位： | 首都师范大学数学科学学院; |
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| 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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| 摘 要： | 对单复变中的Schwarz引理与Schwarz-Pick引理在C~n中的超球上进行了推广.考虑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.
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| 关 键 词： | Schwarz引理 Schwarz-Pick引理 全纯自同构变换 |
Generalization of Schwarz Lemma and Schwarz-Pick Lemma on the Unit Ball B_n |
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| WANG An,SUN Liyan and LIU Ying. Generalization of Schwarz Lemma and Schwarz-Pick Lemma on the Unit Ball B_n[J]. Chinese Annals of Mathematics, 2011, 32(5): 579-592 |
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| Authors: | WANG An SUN Liyan LIU Ying |
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| Affiliation: | WANG An~1 SUN Liyan~2 LIU Ying~1 1 School of Mathematical Sciences,Capital Normal University,Beijing 100048,China. 2 Corresponding author.School of Mathematical Sciences,China. |
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| Abstract: | The Schwarz lemma and the Schwarz-Pick lemma are generalized on the unit ball B_n in C~n.Considering the holomorphic function f(z) whose norm is less than 1 on the unit ball B_n in 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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| Keywords: | Schwarz lemma Schwarz-Pick lemma Holomorphic automorphism transformation |
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