The Landau-type theorem of α-harmonic mapping with a given boundary function in Lebesgue space

The aim of this paper is to obtain several properties of α-harmonic mapping with f∗∈Lp(T) and p∈[1,∞]. After estimating the coefficients of α-harmonic mapping, we give a new Landau-type theorem for this class of mappings, which is a kind of generalization from the case of α=0 to the case α>−1 given by Shi et al. After establishing a Schwarz-Pick type inequality, we also build another Landau-type theorem for the solutions to an inhomogeneous equation Δαf=g, here g:D¯→C is a continuous function.