Weighted integral inequalities for the maximal geometric mean operator in martingales

Under appropriate conditions on Youngʹs functions Φ 1 and Φ 2 , 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 Φ 1 = t p and Φ 2 = t p , the inequalities revert to the ones of strong or weak ( p , p ) -type in martingale spaces.