【摘要】 <正> 一、引言 Hwang证明了“Doob猜测”。他证明在单位圆内部存在这样的亚纯函数f,f在单位圆周上每一点都有细极限,但又以单位圆周上每一点为Julia点。证明之后,Hwang问道,上述结论中的“亚纯”二字可否改为“全纯”?他自已没有解决这个问题。1984更多还原

【Abstract】 The Doob-Hwang problem is generalized and solved as follows:1° If 1<α≤2 and f(z) is holomorphic in the unit disc D and has an α-fine limit at z0∈C (unit circle), then f(z) has an equal non-tangential limit at z0, where "2-fine limit" is meant usual tine limit.2° If 0<α≤1, then there exists a function which is holomorphic in D and has α-limit 0 at every point of C, but takes every point of C as its Julia point.The assertion 1° is established on the fact that the α-fine topology (1<α<2) preserves many properties of the fine topology though the former is strictly finer. It reveals itself a nontrivial extension of Q. R. Gao’s negative answer to Doob-Hwang problem. The assertion 2° is obtained by making use of some techniques developed by Gauthier and Arakelian.更多还原