Atomic decomposition and interpolation for Hardy spaces of noncommutative martingales

We prove that atomic decomposition for the Hardy spaces h 1 and H 1 is valid for noncommutative martingales. We also establish that the conditioned Hardy spaces of noncommutative martingales h p and bmo form interpolation scales with respect to both complex and real interpolations.

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Bibliographic Details
Published in:Journal of functional analysis 2010-04, Vol.258 (7), p.2483-2505
Main Authors: Bekjan, Turdebek N., Chen, Zeqian, Perrin, Mathilde, Yin, Zhi
Format: Article
Language:English
Subjects:
Atoms
Hardy spaces
Interpolation
Noncommutative [formula omitted]-spaces
Noncommutative martingales
Square functions
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Summary:We prove that atomic decomposition for the Hardy spaces h 1 and H 1 is valid for noncommutative martingales. We also establish that the conditioned Hardy spaces of noncommutative martingales h p and bmo form interpolation scales with respect to both complex and real interpolations.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2009.12.006