Weighted integral inequalities for the maximal geometric mean operator in martingales

摘要

Under appropriate conditions on Young's 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=tp, the inequalities revert to the ones of strong or weak (p,p)-type in martingale spaces.