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

TL;DR

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

Contribution

The paper introduces modified kernels to derive growth estimates for subharmonic functions, generalizing existing results for analytic and harmonic functions.

Findings

Subharmonic functions grow slower than y^{1-α}|z|^{m+α} at infinity

Growth estimates apply to a broad class of subharmonic functions

Results extend 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 $u(z)= o(y^{1-\alpha}|z|^{m+\alpha})$ at infinity in the upper half plane ${\bf C}_{+}$, which generalizes the growth properties of analytic functions and harmonic functions.