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Uniformly bounded components of normality

Published online by Cambridge University Press:  01 July 2007

XIAOLING WANG  and
WANG ZHOU
XIAOLING WANG
Affiliation:
Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210046, Jiangsu, China. e-mail: wangxiaoling@vip.163.com
WANG ZHOU
Affiliation:
Department of Statistics and Applied Probability, National University of Singapore, Singapore, 117546. e-mail: stazw@nus.edu.sg
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Abstract

Suppose that f(z) is a transcendental entire function and that the Fatou set F(f)≠∅. Set and where the supremum supU is taken over all components of F(f). If B1(f)<∞ or B2(f)<∞, then we say F(f) is strongly uniformly bounded or uniformly bounded respectively. We show that, under some conditions, F(f) is (strongly) uniformly bounded.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 143 , Issue 1 , July 2007 , pp. 85 - 101
Copyright
Copyright © Cambridge Philosophical Society 2007

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