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arXiv · 2410.12137

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

Bo-Yong Long
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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.

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Bo-Yong Long. 2024-10-16. Boundary behavior of alppha-harmonic functions and their Riesz-Fejer inequalities. https://arxiv.org/abs/2410.12137

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