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Weighted mixed-norm inequality on Doob’s maximal operator and John–Nirenberg inequalities in Banach function spaces

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Abstract

We prove a weighted mixed-norm inequality for the Doob maximal operator on a filtered measure space. We also give some characterizations of martingale BMO spaces in the setting of Banach function spaces. The main method is based on the technique of extrapolation on martingale Banach spaces.

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Acknowledgement

The authors thank the referee for careful reading and useful comments.

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Authors and Affiliations

  1. School of Mathematical Sciences, Yangzhou University, Yangzhou, 225002, China

    W. Chen

  2. Department of Mathematics and Information Technology, The Hong Kong Institute of Education, 10 Lo Ping Road, Tai Po, Hong Kong, China

    K.-P. Ho

  3. School of Mathematical Sciences, Central South University, Changsha, 410075, China

    Y. Jiao & D. Zhou

Authors
  1. W. Chen
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  2. K.-P. Ho
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  3. Y. Jiao
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  4. D. Zhou
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Corresponding author

Correspondence to D. Zhou.

Additional information

Wei Chen is supported by the National Natural Science Foundation of China (11771379), the Natural Science Foundation of Jiangsu Province (BK20161326), the Jiangsu Government Scholarship for Overseas Studies (JS-2017-228) and the School Foundation of Yangzhou University (2016CXJ001).

Dejian Zhou is supported by the National Natural Science Foundation of China (11801573).

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Chen, W., Ho, KP., Jiao, Y. et al. Weighted mixed-norm inequality on Doob’s maximal operator and John–Nirenberg inequalities in Banach function spaces. Acta Math. Hungar. 157, 408–433 (2019). https://doi.org/10.1007/s10474-018-0889-5

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