English

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

Complex Variables 2026-03-13 v1

Abstract

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

Keywords

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

R2 v1 2026-07-01T11:15:47.929Z