Integral mean estimates for $(α,β)$-harmonic functions
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866908881446240256 |
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| author | Wang, Zhi-Gang E, Brindha Valson Vijayakumar, R. |
| author_facet | Wang, Zhi-Gang E, Brindha Valson Vijayakumar, R. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_11449 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Integral mean estimates for $(α,β)$-harmonic functions Wang, Zhi-Gang E, Brindha Valson Vijayakumar, R. Complex Variables 30A10, 30H10, 30C62, 30C55 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. |
| title | Integral mean estimates for $(α,β)$-harmonic functions |
| topic | Complex Variables 30A10, 30H10, 30C62, 30C55 |
| url | https://arxiv.org/abs/2603.11449 |