局部一致有界共轭解析函数族

The Family of Locally Uniformly Bounded Conjugate Analytic Functions

证明了在D上局部一致有界共轭解析函数族T={f(z)}的导函数族T’(?){f^(?)(z)}在D上也局部一致有界;讨论了T={f(z)}局部一致有界性与同等连续的关系,进而证明了其局部一致有界与内闭一致有界等价;最后给出了局部一致有界共轭解析函数列{f_n(z)}_(n=1)~∞关于自列紧的性质。

It is proved in this paper that the family of derived functions T'= {f(z)}of the locally uniformly bounded conjugate analytical family T={f(z)}at D is also locally uniformly bounded at D. The relation between the locally uniformly boundedness and equicontinuity is discussed, and the equivalence of locally uniform boundedness and innerclosed uniform boundedness is proved. Consequently, some properties of the compact in itself of sequence {f_n(z)}~∞_(n=1)of locally uniformly bounded conjugate analytical function are given.