Growth Estimates for a Class of Subharmonic Functions in a Half Plane

Abstract

A class of subharmonic functions represented by the modified kernels are proved to have the growth estimates $u(z)=o(y^{1-\alpha }|z{|}^{m+\alpha })$ at infinity in the upper half plane ${\mathbf{C}}_{+}$, which generalizes the growth properties of analytic functions and harmonic functions.

12 pages