Asymptotic Behaviour for a Class of Subharmonic Functions in a Half Space

Abstract

A class of subharmonic functions are proved to have the growth estimates $u(x)=o(x_n^{1-\frac{\alpha }{p}}|x{|}^{\frac{\gamma }{p}+\frac{n-1}{q}-n+\frac{\alpha }{p}})$ at infinity in the upper half space of ${\mathbf{R}}^n$, which generalizes the growth properties of analytic functions and harmonic functions.

12 pages