B-值鞅Hardy空间与BMO空间的实内插

研究了B值鞅Hardy空间与BMO空间的实内插，并利用所得结果，讨论了鞅Hardy空间的内插空间的共轭问题。     

一类小指标鞅空间的原子分解及其应用

对小指标鞅空间：Ｌｒ（０〈ｐ≤２）建立了原子分解定理。利用原子分解对一些鞅不等式给出了新的简单证明。     

B -valued martingale spaces with small index and atomic decompositions

Some atomic decomposition theorems for Banach-space-valued martingales are established. Using them, the embedding relationships between martingale spaces with small index are discussed. The results obtained here are connected closely with thep-uniform smoothness and q-uniform convexity of Banach space in which the martingales take values.     

Banach值鞅变换算子的有界性

本文运用Banach值鞅不等式和鞅空间的相互嵌入关系．讨论了Banach空间值鞅空间上鞅变换算子L的有界性．并给出了鞅变换算子的有界性与Banach空间几何性质的关系．     

Atomic decompositions of Banach-spacevalued martingales

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) and_ρ 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. Project supported by the National Natural Science Foundation of China (Grant No. 19771063).     

鞅空间的原子分解与有限鞅的稠密性

引入了原子鞅与正则原子鞅概念、并研究了两类Banach空间值鞅Hardy空间的原子分解和有限鞅的稠密性,所得结论揭示了鞅Hardy空间正则原子鞅分解的存在性,有限鞅的稠密性和Banach空间的一致光滑性（或一致凸性）三者之间的内在联系．     

Boundedness of dyadic derivative and Cesáro mean operator on some B-valued martingale spaces

In this article, it is proved that the maximal operator of one-dimensional dyadic derivative of dyadic integral I* and Cesàro mean operator σ* are bounded from the B-valued martingale Hardy spaces pΣα, Dα, pLα, p H#α, pKr to Lα (0 < α < ∞), respectively. The facts show that it depends on the geometrical properties of the Banach space.     

BOUNDEDNESS OF DYADIC DERIVATIVE AND CES(A)RO MEAN OPERATOR ON SOME B-VALUED MARTINGALE SPACES

In this article, it is proved that the maximal operator of one-dimensional dyadic derivative of dyadic integral I* and Cesàro mean operator σ* are bounded from the B-valued martingale Hardy spaces pΣα, Dα, pLα, p H#α, pKr to Lα (0 < α < ∞), respectively. The facts show that it depends on the geometrical properties of the Banach space.     

几类B值小指标鞅空间的原子分解

本文对几类B值小指标鞅空间建立了原子分解定理,利用原子分解讨论了它们之间的相互嵌入关系,其原子分解的存在性和它们之间的关系均与Banach空间的凸性和光滑性有密切联系.     

双参数B值鞅Hardy空间的实内插

利用原子分解方法,研究了双参数Ｂ值鞅Ｈａｒｄｙ空间之间的实内插。     

Atomic Decompositions for Two-Parameter Vector-Valued Martingales and Two-parameter Vector-valued Martingale Spaces

In this paper atomic decompositions for two-parameter vector-valued martingales are given. With the help of the atomic decompositions the relations between the mutual embedding of two-parameter vector-valued martingale spaces and geometric properties of Banach spaces are investigated. Our study shows that geometric properties of Banach spaces determine the embedding of martingale spaces and conversely the latter can characterize the former. This revised version was published online in June 2006 with corrections to the Cover Date.     

鞅空间理论的新进展

本文是一篇综述性的文字,内容主要是近年来有关鞅空间理论的发展状况,特别是集中于B-值鞅和弱型鞅空间两个部分,可以看做是整个鞅空间理论发展的一个侧面.希望以此引起读者对鞅论的了解和进一步研究的兴趣.具体内容分为以下三节:1.研究鞅空间理论的意义,阐述鞅空间理论与调和分析的关系;2.鞅空间理论的向量值化,阐述B-值鞅不等式与Banach空间几何学的相互依存关系;3.弱型鞅空间与变指数鞅空间的不等式及其应用.     

Vector-valued weak martingale Hardy spaces and atomic decompositions

Some atomic decomposition theorems are proved in vector-valued weak martingale Hardy spaces w _p Σ_α(X), w _p Q _α(X) and wD _α(X). As applications of atomic decompositions, a sufficient condition for sublinear operators defined on some vector-valued weak martingale Hardy spaces to be bounded is given. In particular, some weak versions of martingale inequalities for the operators f*, S ^(p)(f) and σ^(p)(f) are obtained. This research was supported by the National Science Foundation of China (No. 10371093).     

鞅空间K（lnK）^q和M（lnM）^q（q〉0）的定义及性质

在鞅的研究中,人们把具有某种相同性质的鞅归为一类,这就形成了许多不同的鞅空间.本文定义了两组新的鞅空间,并给出了这两组鞅空间之间以及它们与已知鞅空间的关系,最后给出了这两组鞅空间的有关性质.     

THE DYADIC DERIVATIVE AND CESARO MEAN OF BANACH-VALUED MARTINGALES

In this article, the Banach space X and the martingales with values in it are considered. It is shown that the maximal operators of the one-dimensional dyadic derivative of the dyadic integral and Cesaro means are bounded from the dyadic Hardy- Lorentz space pH^-ra（X） to Lra（X） when X is isomorphic to a p-uniformly smooth space （1 〈p ≤ 2）. And it is also bounded from Hra（X） to Lra（X） （0 〈 r 〈 ∞,0 〈 a≤oc） when X has Radon-Nikodym property. In addition, some weak-type inequalities are given.     

向量值鞅空间_pH_T~S(X)与_pH_r~σ(X)的共轭

证明了B值鞅空间,pHSr(X)和pHσr(X)的共轭分别是qKSr′(X*)与qKσr′(X*),此外还讨论了pKSr(X)和pKr(X),pKσr(X)和pK+r(X)的相互嵌入关系与Banach空间的p一致光滑性和q一致凸性之间的密切联系.     

B—值鞅的原子分解在内插理论中的一个应用

应用原子分解方法,讨论了一类Ｂａｎａｃｈ空间值鞅Ｈａｒｄｙ空间的实内插,推广了Ｗｅｉｓｚ［３］中的相应结论     

复拟Banach空间的PL一致光滑性及其鞅刻划

本文引进了空间的ＰＬ一致光滑性与复对称鞅，证明了等价赋范定理，得到了一系列关于ＰＬ一致光滑空间的复对称鞅不等式，并应用复对称鞅的大数定律给出了值空间的ＰＬ一致光滑性的刻划。     

鞅空间K(lnK)~q和M(lnM)~q(q>0)的定义及性质

在鞅的研究中,人们把具有某种相同性质的鞅归为一类,这就形成了许多不同的鞅空间.本文定义了两组新的鞅空间,并给出了这两组鞅空间之间以及它们与已知鞅空间的关系,最后给出了这两组鞅空间的有关性质.     

具有AUMD性质的复Banach空间的某些特征

本应用解析鞅的一类特殊的不等式给出了具有AUMD性质的复Banach空间的某些特征。