2025/12/04 by Jinjing Qiao, Qiao, Jinjing, Chang, Jiale +2
Mathematics · #Analytic and geometric function theory #Holomorphic and Operator Theory #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.2512.04379
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 Lp norms of the boundary functions.