Interpolation and the John–Nirenberg inequality on symmetric spaces of noncommutative martingales
Bekjan T.N. Chen Z. Raikhan M. Sun M.
2022Institute of Mathematics. Polish Academy of Sciences
Studia Mathematica
2022#262Issue 3241 - 273 pp.
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 Lp-case. As an application, we provide the atomic decomposition of a noncommutative martingale Hardy space h1 using symmetric atoms as building blocks, and give the boundedness of paraproducts on symmetric spaces of noncommutative martingales.
atomic decomposition , BMO-space , Hardy space , interpolation , John–Nirenberg inequality , noncommutative martingale , noncommutative symmetric spaces
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College of Mathematics and Systems Science, Xinjiang University, Urumqi, 830046, China
Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, 30 West District Xiao-Hong-Shan, Wuhan, 430071, China
Astana IT University, Nur-Sultan, 010000, Kazakhstan
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China
College of Mathematics and Systems Science
Wuhan Institute of Physics and Mathematics
Astana IT University
School of Mathematics and Statistics
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