On some inequalities of local times for Azéma martingales (Q1572828)

The so-called Azéma martingale is the optional projection of a Brownian motion starting at 0 onto the filtration generated by its sign process. In a similar way to the case of Brownian motion, there exists a local time associated with this martingale which gives rise to an occupation density formula. The main result of this paper is a Burkholder-type inequality involving stopping times and space suprema of the local time evaluated at the same time.