Landau's Theorem for Harmonic Bloch Functions on Simply Connected Domains

For alpha is an element of (0,infinity), let B-H,B-Omega(alpha) denote the class of harmonic alpha-Bloch mappings on a proper simply connected domain Omega subset of C. In this article, we study coefficient estimates for harmonic alpha-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 alpha-Bloch space B-H,B-Omega gamma(alpha) on the shifted disk Omega(gamma), where Omega(gamma) :={z is an element of C: |z + gamma/1-gamma| < 1/1-gamma} and 0 <= gamma < 1.