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.

Keywords

Banach-valued martingale Hardy–Lorentz–Karamata space Atomic decomposition Duality Martingale inequality 

Mathematics Subject Classification

Primary: 60G46 Secondary: 60G42 

Notes

Acknowledgements

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

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2018

Authors and Affiliations

  1. 1.School of ScienceHubei University of Automotive TechnologyShiyanChina
  2. 2.School of Mathematics and StatisticsCentral South UniversityChangshaChina
  3. 3.School of ScienceQilu University of TechnologyMudan district, HezeChina

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