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May 2007 Conditioned square functions for noncommutative martingales
Narcisse Randrianantoanina
Ann. Probab. 35(3): 1039-1070 (May 2007). DOI: 10.1214/009117906000000656

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.

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Narcisse Randrianantoanina. "Conditioned square functions for noncommutative martingales." Ann. Probab. 35 (3) 1039 - 1070, May 2007. https://doi.org/10.1214/009117906000000656

Information

Published: May 2007
First available in Project Euclid: 10 May 2007

zbMATH: 1155.46034
MathSciNet: MR2319715
Digital Object Identifier: 10.1214/009117906000000656

Subjects:
Primary: 46L52 , 46L53
Secondary: 46L51 , 60G42

Keywords: martingale inequalities , Noncommutative L^p-spaces , square functions

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.35 • No. 3 • May 2007
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