Abstract
We prove Burkholder’s inequalities in noncommutative Lorentz spaces L p , q ( M ) , 1 > p > ∞ , L^{p,q}(\mathcal {M}), 1>p>\infty , 1 ≤ q > ∞ 1\leq q>\infty , associated with a von Neumann algebra M \mathcal {M} equipped with a faithful normal tracial state. These estimates generalize the classical inequalities in the commutative case.
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