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Real Interpolation Between Strong Martingale Hardy Spaces

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Abstract

In this paper, we establish a decomposition theorem for strong martingale Hardy space \(sH_p^\sigma \), which is based on its atomic decomposition theorem. By using of this decomposition theorem, we investigate the real interpolation spaces between \(sH_p^\sigma \;(0<p\le 1)\) and \(sL_2\). Furthermore, with the help of the decomposition theorem and the real interpolation method, a sufficient condition to ensure the boundedness of a sublinear operator defined on strong martingale Hardy-Lorentz spaces is given.

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Acknowledgements

Jianzhong Lu is supported by the Fundamental Research Funds for the Central University of Central South University (No. 2021zzts0032); Kaituo Liu is supported by the Doctoral Scientific Research Foundation of HuBei University of Automotive Technology Grand BK201805.

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Authors and Affiliations

  1. School of Mathematics, Physics and Optoelectronic Engineering, HuBei University of Automotive Technology, 442002, Shiyan, China

    Kaituo Liu

  2. School of Mathematics and Statistics, Central South University, 410075, Changsha, China

    Jianzhong Lu & Lihua Peng

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  1. Kaituo Liu
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  2. Jianzhong Lu
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  3. Lihua Peng
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Liu, K., Lu, J. & Peng, L. Real Interpolation Between Strong Martingale Hardy Spaces. Acta Math Vietnam 48, 423–443 (2023). https://doi.org/10.1007/s40306-023-00505-5

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