Boundary behavior of alppha-harmonic functions and their Riesz-Fejer inequalities
Complex Variables
2024-10-17 v1
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.
Keywords
Cite
@article{arxiv.2410.12137,
title = {Boundary behavior of alppha-harmonic functions and their Riesz-Fejer inequalities},
author = {Bo-Yong Long},
journal= {arXiv preprint arXiv:2410.12137},
year = {2024}
}
Comments
21pages