Growth Estimates and Integral Representations of Harmonic and Subharmonic Functions

TL;DR

This dissertation explores growth estimates and integral representations of harmonic and subharmonic functions across various domains, extending classical formulas and analyzing their limit behaviors.

Contribution

It generalizes harmonic majorants, Carleman and Nevanlinna formulas, and provides new integral representations for harmonic functions in half planes and half spaces.

Findings

Growth estimates for subharmonic functions established

Generalizations of harmonic majorants and classical formulas achieved

Integral representations for harmonic functions derived

Abstract

There are ten chapters in this dissertation, which focuses on nine contents: growth estimates for a class of subharmonic functions in the half plane; growth estimates for a class of subharmonic functions in the half space; a generalization of harmonic majorants; properties of limit for Poisson integral; a lower bound for a class of harmonic functions in the half space; the Carleman formula of subharmonic functions in the half space; a generalization of the Nevanlinna formula for analytic functions in the right half plane; integral representations of harmonic functions in the half plane; integral representations of harmonic functions in the half space.