Abstract In a previous paper we introduced a new concept, the notion of -martingales and we extended the well-known Doob inequality (for 1 p + ) and the BurkholderDavisGundy inequalities (for p = 2) to -martingales. After showing new Fefferman-type inequalities that involve sharp brackets as well as the space bmoq, we extend the BurkholderDavisGundy inequalities (for 1 p + ) to -martingales. By means of these inequalities we give sufficient conditions for the closedness in Lp of a space of stochastic integrals with respect to a fixed d-valued semimartingale, a question which arises naturally in the applications to financial mathematics. Finally we investigate the relation between uniform convergence in probability and semimartingale topology.