On the roper-suffridge extension operator

被引：1

作者：

Sheng Gong

Taishun Liu

机构：

[1] University of Science and Technology of China Hefei,Department of Mathematics

来源：

Journal d’Analyse Mathématique | 2002年 / 88卷

关键词：

Unit Disk; Extension Operator; Pseudoconvex Domain; Bloch Mapping; Biholomorphic Mapping;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In 1995, Roper and Suffridge defined an extension operator which maps a locally biholomorphic function on the unit diskD in ℂ to a locally biholomorphic mapping on the unit ballBn in ℂn. This extension operator preserves many important properties, e.g., convexity and starlikeness, etc. In this note, we introduce the family ofε starlike mappings, and prove that the Roper-Suffridge extension operator preserves theε starlikeness on some Reinhardt domains. This result includes many known results and solves an open problem of Graham and Kohr.

引用

页码：397 / 404

页数：7

共 15 条

[1] Graham I.(2000)Univalent mappings associated with the Roper-Suffridge extension operator J. Analyse Math. 81 331-342
[2] Kohr G.(2002)An extension theorem and subclass of univalent mappings in several complex variables Complex Variables 47 59-72
[3] Graham I.(2000)Loewner chains and Roper-Suffridge extension operator J. Math. Anal. Appl. 247 448-465
[4] Kohr G.(1997) B Science in China 40A 799-806
[5] Graham I.(1999)An extension theorem and linear invariant families generated by starlike maps Ann. Univ. Marie Curie-Sklodowska Sect. A 53 193-207
[6] Kohr G.(1999) ℂ Complex Variables 40 35-50
[7] Kohr M.(1995) ℂ J. Analyse Math. 65 333-347
[8] Liu T. S.(undefined)undefined undefined undefined undefined-undefined
[9] Zhang W. J.(undefined)undefined undefined undefined undefined-undefined
[10] Pfaltzgraff J.(undefined)undefined undefined undefined undefined-undefined

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