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Journal of the London Mathematical Society Advance Access originally published online on September 16, 2009
Journal of the London Mathematical Society 2009 80(3):627-648; doi:10.1112/jlms/jdp045
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© 2009 London Mathematical Society

A noncommutative Davis’ decomposition for martingales

Mathilde Perrin

Laboratoire de Mathématiques
Université de France-Comté
25030 Besançon cedex
France

We prove an analogue of the classical Davis’ decomposition for martingales in noncommutative Lp-spaces, involving square functions. We also determine the dual space of the noncommutative conditioned Hardy space h1. We further extend this latter result to the case 1 < p < 2.

2000 Mathematics Subject Classification 46L53, 46L52 (primary), 46L51, 60G42 (secondary).

This work was partially supported by the Agence Nationale de Recherche.

Received July 16, 2008; revised May 20, 2009; published online September 16, 2009.


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