半空间中次调和函数的Phragmn-Lindelf定理及应用

Phragmn-Lindelf theorems of subharmonic functions and their applications in the Half space

本文利用调和函数的Carleman公式,结合Levi的方法,在半空间中证明了次调和函数的Phragmn-Lindelf定理.作为Phragmn-Lindelf定理的应用,本文引入了半空间中的C类函数,并且得到了次调和函数属于C类函数的一个充分必要条件,从而推广了Ahlfors和Levi等的经典结果.

In this paper, the Phragmn-Lindelf theorems of subharmonic functions in the half space are proved, by use of the Carleman＇s formula of harmonic functions and the methods of Levi. An explicit expression of weighted mean m（r） for subharmonic functions is also presented. As an application, functions of class C are introduced in the half space and a sufficient and necessary condition of a subharmonic that belongs to the class C is derived, which generalizes some classic results of Ahlfors and Levi.