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

  • W. Chen
  • K.-P. Ho
  • Y. Jiao
  • D. Zhou
Article
  • 15 Downloads

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.

Key words and phrases

mixed-norm inequality weight Doob’s maximal operator extrapolation BMO 

Mathematics Subject Classification

primary 60G46 secondary 60G42 

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Notes

Acknowledgement

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

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesYangzhou UniversityYangzhouChina
  2. 2.Department of Mathematics and Information TechnologyThe Hong Kong Institute of EducationTai Po, Hong KongChina
  3. 3.School of Mathematical SciencesCentral South UniversityChangshaChina

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