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Noncommutative martingale Hardy-Orlicz spaces: Dualities and inequalities

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Abstract

We investigate dualities and inequalities related to noncommutative martingale Hardy-Orlicz spaces. More precisely, for a concave Orlicz function Φ, we characterize the dual spaces of noncommutative martingale Hardy-Orlicz spaces \(H_\Phi ^c\left({\cal R} \right)\) and \({\rm{h}}_\Phi ^c\left({\cal M} \right)\), where \({\cal R}\) denotes a hyperfinite finite von Neumann algebra and \({\cal M}\) is a finite von Neumann algebra. The first duality is new even for classical martingales, which partially answers the problem raised by Conde-Alonso and Parcet (2016). We establish as well asymmetric martingale inequalities associated with Orlicz functions that are p-convex and q-concave for 0 < p ≼ q < 2.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 12125109, 11971484 and 12001541), Natural Science Foundation of Hunan (Grant No. 2021JJ40714) and Changsha Municipal Natural Science Foundation (Grant No. kq2014118). The authors are grateful to the reviewers for their careful reading and helpful comments.

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  1. School of Mathematics and Statistics, Hunan Key Laboratory of Analytical Mathematics and Applications, Central South University, Changsha, 410083, China

    Yong Jiao, Lian Wu & Dejian Zhou

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  1. Yong Jiao
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  2. Lian Wu
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  3. Dejian Zhou
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Correspondence to Dejian Zhou.

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Jiao, Y., Wu, L. & Zhou, D. Noncommutative martingale Hardy-Orlicz spaces: Dualities and inequalities. Sci. China Math. 66, 2081–2104 (2023). https://doi.org/10.1007/s11425-022-2009-4

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