Modified Poisson Kernel and Integral Representation of Harmonic Functions in Half-Plane

In this paper,using a property of the modified Poisson kernel in a half plane,we prove that a harmonic function u(z)in a half plane with its positive part u~+(z)=max{u(z),0}satisfying a slowly growing condition can be represented by its integral in the boundary of the half plane and that its negative part u~-(z)=max{-u(z),0}can be dominated by a similar slowly growing condition.This improves some classical results about harmonic functions in a half-plane.