Some Orlicz-norm inequalities for martingales

In this paper, we show some orlicz-norm inequalities for martingales, which are ΦΦ-extensions of some classical inequalities in martingale HpHp theory. As applications, a new simple proof of Burkholder–Davis–Gundy inequality in Orlicz-norm form is shown, and the equivalence between Orlicz martingale spaces PΦPΦ and QΦQΦ is obtained.