Boundary behavior of alppha-harmonic functions and their Riesz-Fejer inequalities
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909351541735424 |
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| author | Long, Bo-Yong |
| author_facet | Long, Bo-Yong |
| contents | The solutions of a kind of second-order homogeneous partial differential equation are called (real kernel) alpha-harmonic functions. In this paper, the boundary correspondence and boundary behavior of alpha-harmonic functions are studied, and the corresponding Dirichlet problem is solved. As one of its applications, an asymptotic optimal Riesz-Fejer inequality for alpha-harmonic functions is obtained. In addition, the subharmonic properties of alpha-harmonic functions is explored and an optimal radius is obtained. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_12137 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Boundary behavior of alppha-harmonic functions and their Riesz-Fejer inequalities Long, Bo-Yong Complex Variables Primary 31A20 Secondary 31A05, 30H10 The solutions of a kind of second-order homogeneous partial differential equation are called (real kernel) alpha-harmonic functions. In this paper, the boundary correspondence and boundary behavior of alpha-harmonic functions are studied, and the corresponding Dirichlet problem is solved. As one of its applications, an asymptotic optimal Riesz-Fejer inequality for alpha-harmonic functions is obtained. In addition, the subharmonic properties of alpha-harmonic functions is explored and an optimal radius is obtained. |
| title | Boundary behavior of alppha-harmonic functions and their Riesz-Fejer inequalities |
| topic | Complex Variables Primary 31A20 Secondary 31A05, 30H10 |
| url | https://arxiv.org/abs/2410.12137 |