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arXiv · 2603.11449

Integral mean estimates for $(\alpha,\beta)$-harmonic functions

Zhi-Gang Wang·Brindha Valson E·R. Vijayakumar
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Abstract

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

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Zhi-Gang Wang, Brindha Valson E, R. Vijayakumar. 2026-03-12. Integral mean estimates for $(\alpha,\beta)$-harmonic functions. https://arxiv.org/abs/2603.11449

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