Landau's theorem for harmonic Bloch functions on simply connected domains

For α∈ (0, ∞), let BH, 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 BH, Ωγ (α) on the shifted disk Ωγ, where Ωγ: =z∈C: |z+γ1−γ|<11−γ and 0≤γ<1.