锥中调和函数的积分表示

Integral representations of harmonic functions in a cone

本文证明了锥内一类调和函数h,若其正部h+=max{h,0}满足一种增长条件,则h能被其边界值的积分表示.同时证明了其负部h-=max{-h,0}也能被类似的一种增长条件所控制.所得结论推广了解析函数和调和函数在上半空间中关于积分表示的相关结果.

Our aim in this paper is to prove that a harmonic function h in a cone with its positive part h＋ = max{h,0} satisfying a slowly growing condition can be represented by its integral in the boundary of the cone and its negative part h-= max{-h,0} can also be dominated by a similar slowly growing condition,which improves some classical results about analytic and harmonic functions in the upper half space.