解析函数的边界光滑性
Boundary smoothness of analytic functions
摘要：
我们考虑全纯函数在平面的有界开子集上的行为，满足利普希茨条件，指数为$α$，具有$0<α<1$，在一个例外的边界点附近，所有这些功能表现出某种光滑性。具体而言，我们认为抽象的想法有界点导子代数的功能和经典的复杂的衍生物评估作为一个限制的差异concernents之间的关系。我们得到一个结果，适用于，例如，当开集承认一个内部锥在特殊的边界点。
英文摘要：
We consider the behaviour of holomorphic functions on a bounded open subset of the plane, satisfying a Lipschitz condition with exponent $α$, with $0<α<1$, in the vicinity of an exceptional boundary point where all such functions exhibit some kind of smoothness. Specifically, we consider the relation between the abstract idea of a bounded point derivation on the algebra of such functions and the classical complex derivative evaluated as a limit of difference quotients. We obtain a result which applies, for example, when the open set admits an interior cone at the special boundary point.
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