Integral representations of harmonic functions in a cone
Guantie Deng, Lei Qiao · Scientia Sinica Mathematica · 2011
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.