一致有界正规分量
Uniformly bounded components of normality
摘要：
设$f(z)$是一个超越整函数，且法图集$F(f)\neq\emptyset$ .设置$$B_1(f):=\sup_{U}\frac{\sup_{z\in U}\log(|z|+3)}{\inf_{w\in U}\log(|w|+3)}$$和$$B_2(f):=\sup_{U}\frac{\sup_{z\in U}\log\log(|z|+30)}{\inf_{w\in U}\log(|w|+3)},$$，其中上确界$\sup_{U}$在$F(f)$的所有分量上取。如果$B_1(f)<\infty$或$B_2(f)<\infty$，则分别称$F(f)$是强一致有界的或一致有界的.在这篇文章中，我们将证明，在某些条件下，$F(f)$是（强）一致有界的。
英文摘要：
Suppose that $f(z)$ is a transcendental entire function and that the Fatou set $F(f)\neq\emptyset$. Set $$B_1(f):=\sup_{U}\frac{\sup_{z\in U}\log(|z|+3)}{\inf_{w\in U}\log(|w|+3)}$$ and $$B_2(f):=\sup_{U}\frac{\sup_{z\in U}\log\log(|z|+30)}{\inf_{w\in U}\log(|w|+3)},$$ where the supremum $\sup_{U}$ is taken over all components of $F(f)$. If $B_1(f)<\infty$ or $B_2(f)<\infty$, then we say $F(f)$ is strongly uniformly bounded or uniformly bounded respectively. In this article, we will show that, under some conditions, $F(f)$ is (strongly) uniformly bounded.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
