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arXiv · 2512.04379

Properties for ($\alpha,\beta$)-harmonic functions

Jinjing Qiao·Jiale Chang·Antti Rasila
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Abstract

We investigate properties of ($\alpha,\beta$)-harmonic functions. First, we discuss the coefficient estimates for ($\alpha,\beta$)-harmonic functions. In particular, we obtain Heinz's inequality for ($\alpha,\beta$)-harmonic functions, propose a coefficient bound for normalized univalent ($\alpha,\beta$)-harmonic functions and prove that this holds for the subclass that consists of starlike functions. Furthermore, by utilizing the relationship between ($\alpha,\beta$)-harmonic functions and harmonic functions, we obtain Rad\'{o}'s theorem, Koebe type covering theorems and an area theorem. Finally, we show growth estimates and distortion estimates for ($\alpha,\beta$)-harmonic functions by using the $L^p$ norms of the boundary functions.

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Jinjing Qiao, Jiale Chang, Antti Rasila. 2025-12-04. Properties for ($\alpha,\beta$)-harmonic functions. https://arxiv.org/abs/2512.04379

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