Integral mean estimates for $(\alpha,\beta)$-harmonic functions
Complex Variables
2026-03-13 v1
Abstract
We establish sharp integral mean estimates for -harmonic functions on the unit disk. Explicit bounds for the functions and their partial derivatives are obtained in terms of boundary data, by means of the associated Poisson-type kernel and hypergeometric function representations. As applications, we derive coefficient estimates and Hardy space-type results, extending well-known inequalities for classical harmonic and -harmonic functions to the -harmonic setting.
Cite
@article{arxiv.2603.11449,
title = {Integral mean estimates for $(\alpha,\beta)$-harmonic functions},
author = {Zhi-Gang Wang and Brindha Valson E and R. Vijayakumar},
journal= {arXiv preprint arXiv:2603.11449},
year = {2026}
}
Comments
19 pages, comments are welcome