Sharp pointwise estimate of $\alpha -$harmonic functions

Let $\alpha >-1$ and assume that $f$ is $\alpha -$harmonic mapping defined in the unit disk that belongs to the Hardy class $h^p$ with $p\ge 1$. We obtain some sharp estimates of the type $\mathrm{\mid }f(z)\mathrm{\mid }\le g(\mathrm{\mid }r\mathrm{\mid })\mathrm{\parallel }{f}^{\ast }{\mathrm{\parallel }}_p$ and $\mathrm{\mid }Df(z)\mathrm{\mid }\le h(\mathrm{\mid }r\mathrm{\mid })\mathrm{\parallel }{f}^{\ast }{\mathrm{\parallel }}_p$. We also prove a Schwarz type lemma for the class of $\alpha -$harmonic mappings of the unit disk onto itself fixing the origin.