A note on Cantor boundary behavior

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:408

Article

Liu, Jing-Cheng¹  Dong, Xin-Han¹  Peng, Shi-Mao¹ 

[1] Hunan Normal Univ, Coll Math & Comp Sci, Key Lab High Performance Comp & Stochast Informat, Minist Educ China, Changsha 410081, Hunan, Peoples R China

关键词: Cantor boundary behavior;    Infinite Blaschke product;    Pre-Schwarzian derivative;    Integral means;   

DOI  :  10.1016/j.jmaa.2013.06.059

来源: Elsevier

【 摘 要 】

For an analytic function f on the open unit disk ID and continuous on (D) over bar, the Cantor boundary behavior (CBB) is used to describe the curve f(partial derivative D) that forms infinitely many fractal-look loops everywhere. The class of analytic functions with the CBB was formulated and investigated in Dong et al. [6]. In this note, our main objective is to give further discuss of the criteria of CBB in Dong et al. [6]. We show that the two major criteria, the accumulation of the zeros of f'(z) near the boundary and the fast mean growth rate of f'(z) near the boundary, do not imply each other. Also we make an improvement of another criterion, which allows us to have more examples of CBB. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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