Variational characterization of H^p

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 $p\in(\frac n{n+1},1]$.