Variational characterization of H p

Source abstract

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