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B-Valued Martingale Hardy–Lorentz–Karamata Spaces

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Abstract

In this paper, we investigate the Hardy–Lorentz–Karamata spaces for Banach space-valued martingales. Relying on the geometrical properties of the underlying Banach spaces, we establish the atomic decompositions and characterize the dual spaces of these spaces. We also obtain some martingale inequalities in the setting of Hardy–Lorentz–Karamata spaces.

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Acknowledgements

The authors would like to thank the referees and the editors for their valuable suggestions and comments.

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Authors and Affiliations

  1. School of Science, Hubei University of Automotive Technology, Shiyan, 442002, China

    Kaituo Liu & Tian Yue

  2. School of Mathematics and Statistics, Central South University, Changsha, 410085, China

    Kaituo Liu

  3. School of Science, Qilu University of Technology, Mudan district, Heze, 274000, China

    Weiwei Li

Authors
  1. Kaituo Liu
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  2. Weiwei Li
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  3. Tian Yue
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Correspondence to Kaituo Liu.

Additional information

Communicated by Rosihan M. Ali.

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Liu, K., Li, W. & Yue, T. B-Valued Martingale Hardy–Lorentz–Karamata Spaces. Bull. Malays. Math. Sci. Soc. 42, 2395–2422 (2019). https://doi.org/10.1007/s40840-018-0607-z

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  • DOI: https://doi.org/10.1007/s40840-018-0607-z

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