Boundary behavior of alppha-harmonic functions and their Riesz-Fejer inequalities

TL;DR

This paper investigates the boundary behavior and boundary correspondence of alpha-harmonic functions, solves the Dirichlet problem for these functions, and establishes an optimal Riesz-Fejer inequality along with subharmonic properties and radius estimates.

Contribution

It provides new insights into the boundary behavior of alpha-harmonic functions and introduces an asymptotically optimal Riesz-Fejer inequality for them.

Findings

Boundary correspondence and behavior characterized

Dirichlet problem solved for alpha-harmonic functions

Established optimal Riesz-Fejer inequality and radius

Abstract

The solutions of a kind of second-order homogeneous partial differential equation are called (real kernel) alpha-harmonic functions. In this paper, the boundary correspondence and boundary behavior of alpha-harmonic functions are studied, and the corresponding Dirichlet problem is solved. As one of its applications, an asymptotic optimal Riesz-Fejer inequality for alpha-harmonic functions is obtained. In addition, the subharmonic properties of alpha-harmonic functions is explored and an optimal radius is obtained.