Weighted integral inequalities for the maximal geometric mean operator in martingales

Under appropriate conditions on Young's functions Φ1 and Φ2, we give necessary and sufficient conditions in order that weighted integral inequalities hold for the maximal geometric mean operator G in martingale Orlicz classes. When Φ1=tp and Φ2=tp, the inequalities revert to the ones of strong or weak (p,p)-type in martingale spaces.