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Bulletin of the London Mathematical Society 2005 37(2):243-253; doi:10.1112/S0024609304003947
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© London Mathematical Society

On the Best Constants in Some Non-Commutative Martingale Inequalities

Marius Junge and Quanhua Xu

University of Illinois, Department of Mathematics Urbana, IL 61801, USA junge{at}math.uiuc.edu
Université de Franche-Comté, Laboratoire de Mathématiques 25030 Besançcon Cedex, France qx{at}math.univ-fcomte.fr

Received 15 July 2003. Revision received 5 April 2004.

The optimal orders are determined for the best constants in the non-commutative Burkholder–Gundy, Doob and Stein inequalities obtained recently in non-commutative martingale theory. 2000 Mathematics Subject Classification 46L53, 46L51.

Marius Junge is partially supported by the NSF.


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