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

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,Ωγ (α) on the shifted disk Ω γ , where