摘要
In this article,we introduce the martingale Musielak-Orlicz Hardy spaces H_φ^*(■),Pφ(?),H_φ^S(■),Qφ(?)and H_φ^s(■),respectively,via the maximal function,the quadratic variation and the conditional quadratic variation of martingales.We then establish the atomic characterizations of H_φ^s(■),Pφ(■)and Qφ(■).As applications,we obtain the dual space of H_φ^s(■)and several martingale inequalities which further clarify the relations among H_φ^*(■),Pφ(■),H_φ^S(■),Qφ(■)and H_φ^s(■).Especially,as special cases,the results on atomic characterizations of H_φ^s(■),Pφ(?)and Qφ(■)as well as on the dual space of H_φ^s(■)in the weighted case are also new.
In this article,we introduce the martingale Musielak-Orlicz Hardy spaces H_φ~*(?),Pφ(?),H_φ~S(?),Qφ(?)and H_φ~s(?),respectively,via the maximal function,the quadratic variation and the conditional quadratic variation of martingales.We then establish the atomic characterizations of H_φ~s(?),Pφ(?)and Qφ(?).As applications,we obtain the dual space of H_φ~s(?)and several martingale inequalities which further clarify the relations among H_φ~*(?),Pφ(?),H_φ~S(?),Qφ(?)and H_φ~s(?).Especially,as special cases,the results on atomic characterizations of H_φ~s(?),Pφ(?)and Qφ(?)as well as on the dual space of H_φ~s(?)in the weighted case are also new.
基金
supported by National Natural Science Foundation of China (Grant Nos. 11471337, 11722114, 11571039 and 11671185)
