Abstract
We prove a weak-type (1, 1) inequality involving conditioned versions of square functions for martingales in noncommutative Lp-spaces associated with finite von Neumann algebras. As application, we determine the optimal orders for the best constants in the noncommutative Burkholder/Rosenthal inequalities from [Ann. Probab. 31 (2003) 948–995]. We also discuss BMO-norms of sums of noncommuting order-independent operators.
Citation
Narcisse Randrianantoanina. "Conditioned square functions for noncommutative martingales." Ann. Probab. 35 (3) 1039 - 1070, May 2007. https://doi.org/10.1214/009117906000000656
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