INTEGRAL REPRESENTATION OF HARMONIC FUNCTIONS IN A HALF PLANE
Guantie Deng · Journal of Mathematics · 2006
In this paper, we prove that a harmonic function u(z) in a half plane, in case its positive part u+(z) satisfying a slowly growing condition, can be represented by its integral on the boundary of the half plane and that its negative part u-(z) can be dominated by a similar slowly growing condition. For a negative harmonic function in a half plane, our result is some classical one about harmonic functions in a half-plane.