An Equivalent Quasinorm For The Lipschitz Space Of Noncommutative Martingales
OPEN MATHEMATICS(2020)
Abstract
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.
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Key words
noncommutative space, martingale, Hardy space
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