An Equivalent Quasinorm For The Lipschitz Space Of Noncommutative Martingales

In this paper, an equivalent quasinorm for the Lipschitz space of noncommutative martingales is presented. As an application, we obtain the duality theorem between the noncommutative martingale Hardy space h(p)(c)(M) (resp. h(p)(r)(M )) and the Lipschitz space lambda(c)(beta)(M) (resp. lambda(r)(beta)(M )) for 0 < p < 1, beta = 1/p - 1. We also prove some equivalent quasinorms for h(p)(c)(M) and h(p)(r)(M) for p = 1 or 2 < p < infinity.