Several theorems for atomic decompositions of Banach-space-valued martingales are proved. As their applications, the relationship among some martingale spaces such asH α(X) andρ H α in the case 0< α? are studie...Several theorems for atomic decompositions of Banach-space-valued martingales are proved. As their applications, the relationship among some martingale spaces such asH α(X) andρ H α in the case 0< α? are studied. It is shown that there is a close connection between the results and the smoothness and convexity of the value spaces.展开更多
In this article, several weak Hardy spaces of Banach-space-valued martingales are introduced, some atomic decomposition theorems for them are established and their duals are investigated. The results closely depend on...In this article, several weak Hardy spaces of Banach-space-valued martingales are introduced, some atomic decomposition theorems for them are established and their duals are investigated. The results closely depend on the geometrical properties of the Banach space in which the martingales take values.展开更多
In this paper some inequalities for maximal operator and p-power operator of martin-gales with values in Banach spaces are established. We discuss some relationships betweenseveral martingale spaces, and present chara...In this paper some inequalities for maximal operator and p-power operator of martin-gales with values in Banach spaces are established. We discuss some relationships betweenseveral martingale spaces, and present characterizations of convexity and smoothness ofBanach spaces.展开更多
In this article,atomic decompositions and the duals of some B-valued r.v.se- quence spaces are investigated.The results show that it closely depends on the geometrical properties of the sequence that take values in.
Let E be a Banach space with the cl-norm｜｜·｜｜ in E／{0}, and let S（E） = {e ∈ E： ｜｜e｜｜ = 1}. In this paper, a geometry characteristic for E is presented by using a geometrical construct of S（E）. That...Let E be a Banach space with the cl-norm｜｜·｜｜ in E／{0}, and let S（E） = {e ∈ E： ｜｜e｜｜ = 1}. In this paper, a geometry characteristic for E is presented by using a geometrical construct of S（E）. That is, the following theorem holds： the norm of E is of eI in E／{0} if and only if S（E） is a c1 submanifold of E, with codimS（E） = 1. The theorem is very clear, however, its proof is non-trivial, which shows an intrinsic connection between the continuous differentiability of the norm ｜｜·｜｜ in E／{0} and differential structure of S（E）.展开更多
In this article,atomic decompositions and the duals of some B-valued r.v.se- quence spaces are investigated.The results show that it closely depends on the geometrical properties of the sequence that take values in.
The interpolation spaces between Banach space valued martingale Hardy spaces, between Hardy and BMO spaces are identified respectively. Some results obtained here are connected closely with the convexity and smooth...The interpolation spaces between Banach space valued martingale Hardy spaces, between Hardy and BMO spaces are identified respectively. Some results obtained here are connected closely with the convexity and smoothness of the Banach space which the martingales take values in.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 19771063).
文摘Several theorems for atomic decompositions of Banach-space-valued martingales are proved. As their applications, the relationship among some martingale spaces such asH α(X) andρ H α in the case 0< α? are studied. It is shown that there is a close connection between the results and the smoothness and convexity of the value spaces.
基金Supported by the National Natural Foundation of China(10671147)
文摘In this article, several weak Hardy spaces of Banach-space-valued martingales are introduced, some atomic decomposition theorems for them are established and their duals are investigated. The results closely depend on the geometrical properties of the Banach space in which the martingales take values.
文摘In this paper some inequalities for maximal operator and p-power operator of martin-gales with values in Banach spaces are established. We discuss some relationships betweenseveral martingale spaces, and present characterizations of convexity and smoothness ofBanach spaces.
基金Sponsored by the National NSFC under grant No.19771063
文摘In this article,atomic decompositions and the duals of some B-valued r.v.se- quence spaces are investigated.The results show that it closely depends on the geometrical properties of the sequence that take values in.
基金Acknowledgements The author would like to thank Professor Yuwen Wang for telling him that he has considered the relation between smooth Banach space and smooth unit sphere for several years. This work was supported by the National Natural Science Foundation of China （Grant No. 11171151）.
文摘Let E be a Banach space with the cl-norm｜｜·｜｜ in E／{0}, and let S（E） = {e ∈ E： ｜｜e｜｜ = 1}. In this paper, a geometry characteristic for E is presented by using a geometrical construct of S（E）. That is, the following theorem holds： the norm of E is of eI in E／{0} if and only if S（E） is a c1 submanifold of E, with codimS（E） = 1. The theorem is very clear, however, its proof is non-trivial, which shows an intrinsic connection between the continuous differentiability of the norm ｜｜·｜｜ in E／{0} and differential structure of S（E）.
基金Sponsored by the National NSFC under grant No.19771063
文摘In this article,atomic decompositions and the duals of some B-valued r.v.se- quence spaces are investigated.The results show that it closely depends on the geometrical properties of the sequence that take values in.
文摘The interpolation spaces between Banach space valued martingale Hardy spaces, between Hardy and BMO spaces are identified respectively. Some results obtained here are connected closely with the convexity and smoothness of the Banach space which the martingales take values in.
