Martingale Musielak-Orlicz Hardy spaces

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（8）
• 页码范围: 1567-1584
• 页数: 18页
• 语种: 英文

摘要

In this article,we introduce the martingale Musielak-Orlicz Hardy spaces Hφ*(Ω),Pφ(Ω),Hφs(Ω),Qφ (Ω) and Hφ*s (Ω),respectively,via the maximal function,the quadratic variation and the conditional quadratic variation of martingales.We then establish the atomic characterizations of Hφs(Ω),Pφ(Ω) and Qφ(Ω).As applications,we obtain the dual space of Hφs(Ω) and several martingale inequalities which further clarify the relations among Hφ*(Ω),Pφ(Ω),Hφs(Ω),Qφ(Ω) and Hφs(Ω).Especially,as special cases,the results on atomic characterizations of Hφs(Ω),Pφ(Ω) and Qφ(Ω) as well as on the dual space of Hφs(Ω) in the weighted case are also new.