  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 $|f(z)|\le g(|r|) \|f^\ast\|_p$ and
$|Df(z)|\le h(|r|)\|f^\ast\|_p$. We also prove a Schwarz type lemma for the
class of $\alpha-$harmonic mappings of the unit disk onto itself fixing the
origin.
