锥中上调和函数的Riesz分解定理及其应用

The Riesz decomposition theorem for superharmonic functions in a cone and its application

本文给出了锥中上调和函数的Riesz分解定理.同时,得到了它在锥中无穷远点处的增长性质,并且刻画了其例外集的几何性质.作为应用,我们证明了锥内次调和函数的Phragmn-Lindelf型定理.

In this paper, we give the Riesz decomposition theorem for superharmonic functions in a cone. Meanwhile, we obtain the growth properties of them at infinity and characterize the geometrical properties of exceptional sets. As an application, we prove the Phragm@n-LindelSf theorem for subharmonic functions in a cone.