数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (4): 1377-1382.doi: 10.1016/S0252-9602(11)60324-X

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SCHWARZ-PICK ESTIMATES FOR BOUNDED HOLOMORPHIC FUNCTIONS ON CLASSICAL DOMAINS

刘洋1|陈志华2   

  1. 1.Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China;2.Department of Mathematics, Tongji University, Shanghai 200092, China
  • 收稿日期:2009-08-25 修回日期:2010-02-26 出版日期:2011-07-20 发布日期:2011-07-20
  • 基金资助:

    This work was supported by National Natural Science Foundation of China (10871145; 10926066), Doctoral Program Foundation of the Ministry of Education of China (20090072110053) and Natural Science Foundation of Zhejiang Province (Y6100007).

SCHWARZ-PICK ESTIMATES FOR BOUNDED HOLOMORPHIC FUNCTIONS ON CLASSICAL DOMAINS

LIU Xiang1, CHEN Zhi-Hua2   

  1. 1.Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China;2.Department of Mathematics, Tongji University, Shanghai 200092, China
  • Received:2009-08-25 Revised:2010-02-26 Online:2011-07-20 Published:2011-07-20
  • Supported by:

    This work was supported by National Natural Science Foundation of China (10871145; 10926066), Doctoral Program Foundation of the Ministry of Education of China (20090072110053) and Natural Science Foundation of Zhejiang Province (Y6100007).

摘要:

In this paper, Schwarz-Pick estimates for high order Fr´echet derivatives of bounded holomorphic functions on three kinds of classical domains are presented. We generalize the early work on Schwarz-Pick estimates of higher order partial derivatives for bounded holomorphic functions on the disk and unit ball.

关键词: Schwarz-Pick estimate, holomorphic functions, classical domains

Abstract:

In this paper, Schwarz-Pick estimates for high order Fr´echet derivatives of bounded holomorphic functions on three kinds of classical domains are presented. We generalize the early work on Schwarz-Pick estimates of higher order partial derivatives for bounded holomorphic functions on the disk and unit ball.

Key words: Schwarz-Pick estimate, holomorphic functions, classical domains

中图分类号: 

  • 32A10