Properties for ($α,β$)-harmonic functions
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914457063522304 |
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| author | Qiao, Jinjing Chang, Jiale Rasila, Antti |
| author_facet | Qiao, Jinjing Chang, Jiale Rasila, Antti |
| contents | We investigate properties of ($α,β$)-harmonic functions. First, we discuss the coefficient estimates for ($α,β$)-harmonic functions. In particular, we obtain Heinz's inequality for ($α,β$)-harmonic functions, propose a coefficient bound for normalized univalent ($α,β$)-harmonic functions and prove that this holds for the subclass that consists of starlike functions. Furthermore, by utilizing the relationship between ($α,β$)-harmonic functions and harmonic functions, we obtain Radó's theorem, Koebe type covering theorems and an area theorem. Finally, we show growth estimates and distortion estimates for ($α,β$)-harmonic functions by using the $L^p$ norms of the boundary functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04379 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Properties for ($α,β$)-harmonic functions Qiao, Jinjing Chang, Jiale Rasila, Antti Complex Variables Primary: 30C45, 30C50, 31A05, Secondary: 30B10, 30H10 We investigate properties of ($α,β$)-harmonic functions. First, we discuss the coefficient estimates for ($α,β$)-harmonic functions. In particular, we obtain Heinz's inequality for ($α,β$)-harmonic functions, propose a coefficient bound for normalized univalent ($α,β$)-harmonic functions and prove that this holds for the subclass that consists of starlike functions. Furthermore, by utilizing the relationship between ($α,β$)-harmonic functions and harmonic functions, we obtain Radó's theorem, Koebe type covering theorems and an area theorem. Finally, we show growth estimates and distortion estimates for ($α,β$)-harmonic functions by using the $L^p$ norms of the boundary functions. |
| title | Properties for ($α,β$)-harmonic functions |
| topic | Complex Variables Primary: 30C45, 30C50, 31A05, Secondary: 30B10, 30H10 |
| url | https://arxiv.org/abs/2512.04379 |