Martingale Musielak-Orlicz Hardy spaces

被引：22
|
作者：
Xie, Guangheng [1 ]
Jiao, Yong [2 ]
Yang, Dachun [1 ]
机构：
[1] Beijing Normal Univ, Sch Math Sci, Minist Educ China, Lab Math & Complex Syst, Beijing 100875, Peoples R China
[2] Cent South Univ, Sch Math & Stat, Changsha 410075, Hunan, Peoples R China
来源：
SCIENCE CHINA-MATHEMATICS | 2019年 / 62卷 / 08期
基金：
中国国家自然科学基金;
关键词：
martingale; Musielak-Orlicz Hardy space; maximal function; quadratic variation; conditional quadratic variation; atom; duality; LORENTZ SPACES; HP-SPACES; INEQUALITIES; LEBESGUE;
D O I：
10.1007/s11425-017-9237-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we introduce the martingale Musielak-Orlicz Hardy spaces H-phi*(Omega), P-phi(Omega), H-phi(S)(Omega), Q(phi)(Omega) and H-phi(s)(O), respectively, via the maximal function, the quadratic variation and the conditional quadratic variation of martingales. We then establish the atomic characterizations of H-phi(s)(Omega), P-phi(Omega) and Q(phi)(Omega). As applications, we obtain the dual space of H-phi(s)(Omega) and several martingale inequalities which further clarify the relations among H-phi*(Omega), P-phi(Omega), H-phi(S)(Omega), Q(phi)(Omega) and H-phi(s)(Omega). Especially, as special cases, the results on atomic characterizations of H-phi(s)(Omega), P-phi(Omega) and Q(phi)(Omega) as well as on the dual space of H-phi(s)(Omega) in the weighted case are also new.
引用
收藏
页码：1567 / 1584
页数：18
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