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1.
具有无条件鞅差性质的空间   总被引:2,自引:0,他引:2  
近年来,Aldous,Burkholder,Maurey,Pisier,Bourgain 等定义并研究了具有无条件鞅差性质的空间.Banach 空间 X 称为是具有无条件鞅差性质的(记为 X∈UMD),如果 L_p(X)(1相似文献   

2.
关于复Banach空间的几何学   总被引:10,自引:0,他引:10  
本文介绍复Banach空间几何学近年来的发展状况及其与向量值调和分析、B值鞅理论的联系。文章包括以下内容:1.几个反例;2.复凸性与复凸模;3.解析Radon-Nikodym性质的分析特征;4.解析Radon-Nikodym性质的几何特征;5.几种RN性质的比较;6.PL一致凸性的鞅刻画;7.H一致凸性的鞅刻画;8.向量值Hardy与Paley不等式;9.解析UMD空间。  相似文献   

3.
讨论向量值函数的Banach代数L∞(T;X)的极大理想空间的拓扑性质和代数性质,得到了若干结果;给出了Banach空间H∞(D;X)中闭单位球的端点的一条性质.  相似文献   

4.
讨论向量值函数的Banach代数H∞(D;X)的极大理想空间的拓扑性质和代数性质,得到了若干结果.  相似文献   

5.
证明了由m个Lμp空间产生的Banach向量空间(Lμp)m的弱Banach-Saks性质,其中m是自然数, 1 p 〈+∞.当m= 1时,这就是著名的Banach-Saks-Szlenk定理.运用该性质,还给出了定义在向量空间Rm的一个凸集上的非负连续凸函数与取值在空间(Lpμ)m的一个弱紧子集中的向量值函数的复合函数的积分不等式.当这些向量值函数属于由m个Lμ∞空间产生的积空间(Lμ∞)m的一个弱*紧子集时,类似的积分不等式还是成立的.  相似文献   

6.
讨论向量值函数的Banach代数H^∞(D;X)的极大理想空间的拓扑性质和代数性质,得到了若干结果。  相似文献   

7.
设E(X)和F(Y)是向量值序列空间并且E(X)具有弱滑脊性质.A=[Aij]是一个算子值无穷矩阵并且映E(X)进入F(Y).如果(X,Y)有Banach-Steinhaus性质,那么A是σ(E(X),E(X)βY)-σ(F(Y),F(Y)βY)连续的.  相似文献   

8.
石峰 《数学杂志》1994,14(1):77-82
本文探讨了一类近于lp(Co)的Banach空间lp([0,1])(p=0;1≤p≤∝)的几种几何性质,得到了些令人满意的结果,如l∞具有MAP,lp([0,1])(p=0;1≤p≤∝)具有primary性质而无Prime性质。  相似文献   

9.
方习年 《数学杂志》2001,21(1):38-44
本文通过引入B-NUC Banach空间及WB性质,进一步研究Banach-Saks性质(BSP)与近一致凸及紧完全凸性之间的关系。得到以下主要结果。1)Banach空间X具有WB性质当且仅当X具有WBanach-Saks性质(WBSP);2)X是B-NUC空间当且仅当X是具BSP的NUC空间;3)若X具BSP及(H)性质,则X是CωR空间(紧完全ω-凸空间)。  相似文献   

10.
黄旭剑  谭冬妮 《数学学报》2015,58(6):1001-1008
研究向量值空间中的几何酉元.通过数值指标理论刻画向量值空间C(Ω,X),L_∞(μ,X)和L(l_1(Γ),X)中几何酉元的特征,其中X是Banach空间,Ω是紧Hausdorff空间,μ是σ有限测度以及Γ是非空指标集.同时,描述了Banach空间的内射张量积和投射张量积中几何酉元的特征.  相似文献   

11.
《Quaestiones Mathematicae》2013,36(2):111-136
The UMD property of a Banach space is one of the most useful properties when one thinks about possible applications. This is in particular due to the boundedness of the vector-valued Hilbert transform for functions with values in such a space. Looking at operators instead of at spaces, it is easy to check that the summation operator does not have the UMD property. The actual asymptotic behavior however of the UMD constants computed with martingales of length n is unknown. We explain, why it would be important to know this behavior, rephrase the problem of finding these UMD constants and give some evidence of how they behave asymptotically.  相似文献   

12.
刘培德 《数学杂志》2017,37(3):445-456
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.  相似文献   

13.
In this paper the operator-valued martingale transform inequalities in rearrangement invariant function spaces are proved. Some well-known results are generalized and unified. Applications are given to classical operators such as the maximal operator and the p-variation operator of vector-valued martingales, then we can very easily obtain some new vector-valued martingale inequalities in rearrangement invariant function spaces. These inequalities are closely related to both the geometrical properties of the underlying Banach spaces and the Boyd indices of the rearrangement invariant function spaces. Finally we give an equivalent characterization of UMD Banach lattices, and also prove the Fefferman-Stein theorem in the rearrangement invariant function spaces setting.  相似文献   

14.
In this paper, we introduce weighted vector-valued Morrey spaces and obtain some estimates for vector-valued commutators on these spaces. Applications to Calderón-Zygmund singular integral operators, oscillatory singular integral operators and parabolic difference equations are considered.  相似文献   

15.
The paper provides new characterisations of generators of cosine functions and C 0-groups on UMD spaces and their applications to some classical problems in cosine function theory. In particular, we show that on UMD spaces, generators of cosine functions and C 0-groups can be characterised by means of a complex inversion formula. This allows us to provide a strikingly elementary proof of Fattorini’s result on square root reduction for cosine function generators on UMD spaces. Moreover, we give a cosine function analogue of McIntosh’s characterisation of the boundedness of the H functional calculus for sectorial operators in terms of square function estimates. Another result says that the class of cosine function generators on a Hilbert space is exactly the class of operators which possess a dilation to a multiplication operator on a vector-valued L 2 space. Finally, we prove a cosine function analogue of the Gomilko-Feng-Shi characterisation of C 0-semigroup generators and apply it to answer in the affirmative a question by Fattorini on the growth bounds of perturbed cosine functions on Hilbert spaces.  相似文献   

16.
We consider multiparameter singular integrals and pseudodifferential operators acting on mixed-norm Bochner spaces Lp1,…,pN(Rn1×?×RnN;X) where X is a UMD Banach space satisfying Pisier's property (α). These geometric conditions are shown to be necessary. We obtain a vector-valued version of a result by R. Fefferman and Stein, also providing a new, inductive proof of the original scalar-valued theorem. Then we extend a result of Bourgain on singular integrals in UMD spaces with an unconditional basis to a multiparameter situation. Finally we carry over a result of Yamazaki on pseudodifferential operators to the Bochner space setting, improving the known vector-valued results even in the one-parameter case.  相似文献   

17.
We introduce triplet spaces for symmetric relations with defect index (1, 1) in a Pontryagin space. Representations of Pontryagin spaces by spaces of vector-valued analytic functions are investigated. These concepts are used to study 2×2-matrix valued analytic functions which satisfy a certain kernel condition.  相似文献   

18.
Morrey Spaces for Non-doubling Measures   总被引:6,自引:0,他引:6  
The authors give a natural definition of Morrey spaces for Radon measures which may be non-doubling but satisfy certain growth condition, and investigate the boundedness in these spaces of some classical operators in harmonic analysis and their vector-valued extension.  相似文献   

19.
We improve the vector-valued Marcinkiewicz multiplier theorem in a subclass of UMD spaces (introduced by Berkson, Gillespie and Torrea), where Rubio de Francia’s generalized Littlewood–Paley inequality is valid. Received: 10 October 2005; revised: 7 December 2005  相似文献   

20.
We give a characterization of invariant subspaces of finite codimension in Banach spaces of vector-valued analytic functions in several variables, where invariant refers to invariance under multiplication by any polynomial. We obtain very weak conditions under which our characterization applies, that unifies and improves a number of previous results. In the vector-valued case, the results are new even for one complex variable. As a concrete application in several variables, we consider the Bergman space on a strictly pseudo-convex domain, and we improve previous results (assuming C-boundary) to the case of C2-boundary.  相似文献   

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