A remark on John – Nirenberg theorem for martingales - Li, L. (Ukrains’kyi Matematychnyi Zhurnal, 2018)
This paper is mainly devoted to establishing an extension of the John – Nirenberg theorem for martingales, more precisely,let $1 < p < ∞$ and $0 < q < ∞$. If the stochastic basis $(\scr {F_n})_n≥ 0$ is regular, then $BMO_{p,q} = BMO_1$ with the equivalentnorms. Our method is to use a new atomic decomposition construction of the martingale Hardy space.