Weak martingale Hardy spaces and weak atomic decompositions

作     者：HOU Youliang & REN Yanbo School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China Department of Mathematics & Physics, Henan University of Science and Technology, Luoyang 471003, China 

作者机构：School of Mathematics and Statistics Wuhan University Wuhan China Department of Mathematics & Physics Henan University of Science and Technology Luoyang China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2006年第49卷第7期

页      面：912-921页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：This work was supported by National Natural Science Foundation of China (Grant No. 10371093) 

主　　题：martingale, weak Hardy space, weak atom, atomic decomposition. 

摘      要：In this paper we define some weak martingale Hardy spaces and three kinds of weak atoms. They are the counterparts of martingale Hardy spaces and atoms in the classical martingale Hp-theory. And then three atomic decomposition theorems for martingales in weak martingale Hardy spaces are proved. With the help of the weak atomic decompositions of martingale, a sufficient condition for a sublinear operator defined on the weak martingale Hardy spaces to be bounded is given. Using the sufficient condition, we obtain a series of martingale inequalities with respect to the weak Lp-norm, the inequalities of weak (p ,p)-type and some continuous imbedding relationships between various weak martingale Hardy spaces. These inequalities are the weak versions of the basic inequalities in the classical martingale Hp-theory.