  This paper provides a study of several problems related to Hardy spaces left
by G.Weiss in [4]. First, we will prove that the Hardy spaces
$H^p(\mathbb{R}^n)$($0<p\leq1$) can be characterized by the ipschitz function.
Second, we will also prove that there exists a $H^p_\phi(\mathbb{R})$ such that
$H^p(\mathbb{R}) \subsetneq H^p_\phi(\mathbb{R})$ for $0<p\leq1$.
