Integral mean estimates for $(α,β)$-harmonic functions

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Zhi-Gang Wang, Brindha Valson E, R. Vijayakumar
DOI: 10.48550/arxiv.2603.11449
Cited by: 0
References: 3

Abstract

We establish sharp $L^p$ integral mean estimates for $(α,β)$-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 $α$-harmonic functions to the $(α,β)$-harmonic setting.

Fields of Study & Subjects

Analytic and geometric function theory Holomorphic and Operator Theory Mathematical Inequalities and Applications

Publication details

Journal / source
arXiv (Cornell University)
Publication date
12 March 2026
Language
EN
Document type
Preprint