John-Nirenberg inequalities for column martingale BMO spaces

Recently, we have made some progresses on John-Nirenberg theorems for BMO/Lipschitz spaces in the noncommutative martingale setting. In particular, we solved two questions originated from the seminal papers on noncommutative martingale due to Gilles Pisier, Quanhua Xu and Marius Junge. In this talk, I shall overview briefly noncommutative martingale theory and then present our results. Based on joint works with Tao Mei, Congbian Ma, Yu Wang.