数学物理学报(英文版)

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THE EXTENSION OPERATOR IN BANACH SPACES FOR LOCALLY BIHOLOMORPHIC MAPPINGS

刘名生; 朱玉灿   

  1. 华南师范大学数学系, 广州 510631
  • 收稿日期:2004-05-31 修回日期:2007-06-21 出版日期:2008-07-20 发布日期:2008-07-20
  • 通讯作者: 刘名生
  • 基金资助:

    This research is partly supported by the National Natural Science Foundation of China (10471048), the Doctoral Foundation of the Education Committee of
    China (20050574002), the Natural Science Foundation of Fujian Province, China (Z0511013), and the Education Commission Foundation of Fujian Province, China (JB04038)

THE EXTENSION OPERATOR IN BANACH SPACES FOR LOCALLY BIHOLOMORPHIC MAPPINGS

Liu Mingsheng; Zhu Yucan   

  1. Department of Mathematics, South China Normal University, Guangzhou 510631, China
  • Received:2004-05-31 Revised:2007-06-21 Online:2008-07-20 Published:2008-07-20
  • Contact: Liu Mingsheng

摘要:

In this article, the generalized Roper--Suffridge extension operator in Banach spaces for locally biholomorphic mappings is introduced. It is proved that this operator preserves the starlikeness on some domains in Banach spaces but does not preserves convexity for some cases. Moreover, the growth theorem,
covering theorem, and the radius of starlikeness are discussed. Some results of Roper and Suffridge, Gong and Liu, Graham et al in Cn are extended to Hilbert spaces or Banach spaces.

关键词: Biholomorphic starlike mapping, biholomorphic convex mapping, the Roper--Suffridge extension operator

Abstract:

In this article, the generalized Roper--Suffridge extension operator in Banach spaces for locally biholomorphic mappings is introduced. It is proved that this operator preserves the starlikeness on some domains in Banach spaces but does not preserves convexity for some cases. Moreover, the growth theorem,
covering theorem, and the radius of starlikeness are discussed. Some results of Roper and Suffridge, Gong and Liu, Graham et al in Cn are extended to Hilbert spaces or Banach spaces.

Key words: Biholomorphic starlike mapping, biholomorphic convex mapping, the Roper--Suffridge extension operator

中图分类号: 

  • 32H02