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Interpolation and the John–Nirenberg inequality on symmetric spaces of noncommutative martingales

Volume 262 / 2022

Turdebek N. Bekjan, Zeqian Chen, Madi Raikhan, Mu Sun Studia Mathematica 262 (2022), 241-273 MSC: Primary 46L52; Secondary 47L05. DOI: 10.4064/sm200508-11-12 Published online: 2 September 2021


We prove various John–Nirenberg inequalities on symmetric spaces of noncommutative martingales, including the crude and fine versions, which extend the corresponding results of Junge and Musat (2007) and Hong and Mei (2012) in the $L_p$-case. As an application, we provide the atomic decomposition of a noncommutative martingale Hardy space $\mathsf h _1$ using symmetric atoms as building blocks, and give the boundedness of paraproducts on symmetric spaces of noncommutative martingales.


  • Turdebek N. BekjanCollege of Mathematics
    and Systems Science
    Xinjiang University
    Urumqi 830046, China
  • Zeqian ChenWuhan Institute of Physics and Mathematics
    Chinese Academy of Sciences
    30 West District
    Xiao-Hong-Shan, Wuhan 430071, China
  • Madi RaikhanAstana IT University
    Nur-Sultan 010000, Kazakhstan
  • Mu SunSchool of Mathematics and Statistics
    Huazhong University of Science and Technology
    Wuhan 430074, China

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