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

TL;DR

This paper establishes growth estimates for a class of subharmonic functions in a half space, extending known properties of analytic and harmonic functions to a broader class.

Contribution

It introduces a new class of subharmonic functions with growth estimates, generalizing previous results for analytic and harmonic functions.

Findings

Subharmonic functions grow slower than x_{n}^{1-alpha}|x|^{m+alpha} at infinity.

The growth estimates apply to functions represented by modified kernels.

Generalizes classical growth properties of harmonic and analytic functions.

Abstract

A class of subharmonic functions represented by the modified kernels are proved to have the growth estimates u(x) =o(x_{n}^{1-alpha}|x|^{m+alpha})at infinity in the upper half space of Rn, which generalizes the growth properties of analytic functions and harmonic functions.