Zygmund定理一个推广

Promoting a Zygmund Theorem

任福尧在Zygmund函数基础上定义了Λ**函数,并获得Λ**函数的充分必要条件.该文讨论复数域C上一种新的Zygmund型函数类Λp**函数.运用类比Λ**函数的充要条件证明方法,证明了Λp**函数的p次积分平均值的充要条件,即属于平行推广,这些结论具有重要的理论意义,进一步丰富Zygmund函数类的理论.

Ren Fuyao defines Λ＊＊function on the basis of the Zygmund function,and obtains necessary and sufficient conditions for Λ＊＊function.In the paper we discuss the necessary and sufficient conditions for the issue of a new class of functions of Zygmund typeΛp＊＊function on the complex field C.The use ofΛ＊＊function analog proof necessary and sufficient conditions to give proof of the p-th integral average valueΛp＊＊functions necessary and sufficient conditions that belong to parallel promotion,these conclusions are important theoretical significance,thus enriching the theory Zygmund function classes.