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 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, 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
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
Let X be a complex quasi Banach space and Φ:[0,∞)→[0,∞) an increasing convex function with Φ(0)=0 , lim t→∞Φ(t)=∞ and Φ∈Δ 2 . Then L * Φ(X) is a quasi Banach space with contin...Let X be a complex quasi Banach space and Φ:[0,∞)→[0,∞) an increasing convex function with Φ(0)=0 , lim t→∞Φ(t)=∞ and Φ∈Δ 2 . Then L * Φ(X) is a quasi Banach space with continuous quasi norm and L * Φ(X) has the ARNP if and only if X does.展开更多
In this paper we prove the following Hajek Renyi inequality:Let 0<p≤1 ,then for any Banach space B , any L p integrable B valued random variable sequence {D n,n≥1} ,any real number sequence {b...In this paper we prove the following Hajek Renyi inequality:Let 0<p≤1 ,then for any Banach space B , any L p integrable B valued random variable sequence {D n,n≥1} ,any real number sequence {b n,n≥1} with 0<b n↑∞ ,any integer n≥1 ,there exits a constant C=C p>0 (only depending on p ) such thatP( sup j≥nji=1D ib j≥ε)≤Cε -p (∞j=n+1E‖D j‖ pb p j+nj=1E‖D j‖ pb p n) In the other direction,we prove some strong laws of large numbers and the integrability of the maximal functions for B valued random variable sequences by using this inequality and the Hajeck Renyi inequality we have obtained recently.Some known results are extended and improved.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.
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.
文摘Let X be a complex quasi Banach space and Φ:[0,∞)→[0,∞) an increasing convex function with Φ(0)=0 , lim t→∞Φ(t)=∞ and Φ∈Δ 2 . Then L * Φ(X) is a quasi Banach space with continuous quasi norm and L * Φ(X) has the ARNP if and only if X does.
文摘In this paper we prove the following Hajek Renyi inequality:Let 0<p≤1 ,then for any Banach space B , any L p integrable B valued random variable sequence {D n,n≥1} ,any real number sequence {b n,n≥1} with 0<b n↑∞ ,any integer n≥1 ,there exits a constant C=C p>0 (only depending on p ) such thatP( sup j≥nji=1D ib j≥ε)≤Cε -p (∞j=n+1E‖D j‖ pb p j+nj=1E‖D j‖ pb p n) In the other direction,we prove some strong laws of large numbers and the integrability of the maximal functions for B valued random variable sequences by using this inequality and the Hajeck Renyi inequality we have obtained recently.Some known results are extended and improved.
