Sharp pointwise estimate of -harmonic functions

Let >-1 and assume that f is -harmonic mapping defined in the unit disk that belongs to the Hardy class hᵖ with p 1. We obtain some sharp estimates of the type |f (z) | g (|r|) \|f^\|ₚ and |Df (z) | h (|r|) \|f^\|ₚ. We also prove a Schwarz type lemma for the class of -harmonic mappings of the unit disk onto itself fixing the origin.