  In this paper we obtain the variational characterization of Hardy space $H^p$
for $p\in(\frac n{n+1},1]$ and get estimates for the oscillation operator and
the $\lambda$-jump operator associated with approximate identities acting on
$H^p$ for $p\in(\frac n{n+1},1]$. Moreover, we give counterexamples to show
that the oscillation and $\lambda$-jump associated with some approximate
identity can not be used to characterize $H^p$ for $p\in(\frac n{n+1},1]$.
