Abstract
For α ∈ ( 0 , ∞ ) , let B H , Ω ( α ) denote the class of harmonic α-Bloch mappings on a proper simply connected domain Ω ⊆ C . In this article, we study coefficient estimates for harmonic α-Bloch mappings on a proper simply connected domain containing the unit disk. Furthermore, we establish the Landau's theorem and coefficient estimates for the harmonic α-Bloch space B H , Ω γ ( α ) on the shifted disk Ω γ , where Ω γ := { z ∈ C : | z + γ 1 − γ | < 1 1 − γ } and 0 ≤ γ < 1 .
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