Integral Representation of Harmonic Function in a Half-Plane

Abstract:

      In this article, we consider the integral representation of harmonic functions. 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 of a measure on the boundary of the half plan.