C^n空间中单位球上的函数的解析开拓

THE ANALYTIC EXTENSION FOR FUNCTIONS ON THE UNIT BALL IN C￣n

本文证明了定义在Ｂｎ＝｛｜ｚ｜＝１｝上的Ｃα类函数可解析开拓到Ｂｎ＝｛｜ｚ｜＜１｝内的一个充要条件．对于满足一定条件的Ｃα（Ｂｎ）类及Ｃ１（Ｂｎ）类函数，构造了Ｂｎ外分片解析，满足Ｐｌｅｍｅｌｊ公式的Ｃａｕｃｈｙ型积分．

In this paper we show a necessary and sufficient condition that a function f(z) defined on Bn={|z|=1} and belonged to the class Cα(Bn) can be extended to be analytic in Bn={|z|<1}. When u(z) belongs to the class C1(Bn) as well as the class Cα(Bn) and satisfies some conditions, we respectively construct the Cauchy-type integrals which are analytic out of Bn and satisfy the Plemelj formula.