Interpolation and the John–Nirenberg inequality on symmetric spaces of noncommutative martingales
Volume 262 / 2022
Studia Mathematica 262 (2022), 241-273
MSC: Primary 46L52; Secondary 47L05.
DOI: 10.4064/sm200508-11-12
Published online: 2 September 2021
Abstract
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.
