Uniformly bounded components of normality

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Duration: 3 min 30 s
Description: Abstract Suppose that f ( z ) is a transcendental entire function and that the Fatou set F ( f )≠∅. Set and where the supremum sup U is taken over all components of F ( f ). If B 1 ( f )&lt;∞ or B 2 ( f )&lt;∞, 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.
Xiaoling Wang; Wang Zhou
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