Martingale Spaces H 1 and BMO
Sheng-wu He, Jia-gang Wang, Jia-an Yan · 2019
The contents of this chapter belong to the fine and difficult parts of modern martingale theory. The terms, spaces Hardy (H 1 ) and bounded mean osculation (BMO) are borrowed from modern analysis. Fefferman’s inequality is the most important result concerning H 1 - and BMO-martingales. It is much deeper than Kunita-Watanabe inequality. The chapter provides useful information on characterization for BMO-martingales and describes about Davis inequality, Burkholder-Davis-Gundy inequality with theorems and lemmas.