Weak Orlicz space and its applications to the martingale theory  

作　　者：LIU PeiDe,HOU YouLiang & WANG MaoFa School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China 

出　　处：《Science China Mathematics》2010年第4期905-916,共12页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.10671147)

摘　　要：In this paper,the weak Orlicz space wL Φ is introduced and its applications to the martingale theory are discussed.In particular,a series of martingale inequalities including the maximal function inequality in weak Orlicz spaces are established;the relationships between these spaces are investigated.Moreover,the boundedness of several sublinear operators from one weak Orlicz space to another is proved;their vector-valued analogues are also considered.In this paper,the weak Orlicz space wL Φ is introduced and its applications to the martingale theory are discussed.In particular,a series of martingale inequalities including the maximal function inequality in weak Orlicz spaces are established;the relationships between these spaces are investigated.Moreover,the boundedness of several sublinear operators from one weak Orlicz space to another is proved;their vector-valued analogues are also considered.

关 键 词：WEAK ORLICZ SPACE MAXIMAL function MARTINGALE SPACE MARTINGALE INEQUALITY 

分 类 号：O211.6[理学—概率论与数理统计]