ABSTRACT
The contents of this chapter belong to the fine and difficult parts of modern martingale theory. The terms, spaces Hardy (H1) and bounded mean osculation (BMO) are borrowed from modern analysis. Fefferman’s inequality is the most important result concerning H1- 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.
