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Burkholder's inequalities in noncommutative Lorentz spaces

Author: Yong Jiao
Journal: Proc. Amer. Math. Soc. 138 (2010), 2431-2441
MSC (2000): Primary 46L53; Secondary 60G42
Published electronically: March 24, 2010
Previous version: Original version posted March 4, 2010
Corrected version: Current version corrects publisher's error in listing order of author's affiliations
MathSciNet review: 2607873
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Abstract | References | Similar Articles | Additional Information

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

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Additional Information

Yong Jiao
Affiliation: Laboratoire de Mathématiques, Université de Franche-Comté, 25030 Besançon Cedex, France
Address at time of publication: Institute of Probability and Statistics, Central South University, Changsha 410075, People’s Republic of China

Keywords: Noncommutative martingales, Burkholder's inequalities, Lorentz spaces.
Received by editor(s): January 13, 2009
Received by editor(s) in revised form: September 22, 2009
Published electronically: March 24, 2010
Additional Notes: The author was partially supported by the Agence Nationale de Recherche (06-BLAN-0015), the National Natural Science Foundation of China (10671147) and the China Scholarship Council (2007U13085).
Communicated by: Marius Junge
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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