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1.
利用拓扑学的一般理论,研究了序列位差空间的连通性,给出了序列位差空间为可分空间、紧致空间的充分必要条件.  相似文献   

2.
本文建立局部凸拓扑向量空间的正规性、完全正规性和单调正规性的等价条件.作为这些结果的应用,研究了函数空间的单调正规性和可度量性.  相似文献   

3.
彭良雪  林寿 《数学学报》2003,46(6):1225-123
本文回答了关于MCM空间遗传性的一个问题,讨论了k-MCM空间是k半层空间的条件,得到了一些用g函数刻划的度量化定理.主要结论有:MCM空间是关于Fσ子空间遗传的;在正规空间类中,q空间(ωN空间,k-MCM空间)是关于开Fσ子空间遗传的;如果X是具有Gδ对角线的正则次中紧 k-MCM空间,则X是k半层空间;X是可度量化空间的充要条件是存在X上的g函数满足对X中任意不相交的闭集F与紧集C,都有某个n∈ω,使得(∪x∈F g(n,x))∩(∪y∈C g(n,y))=(?).  相似文献   

4.
引进了和内积空间没有相互包含关系的一类新空间:超积空间,进而研究了超积空间的性质.这类新的线性空间具有许多内积空间的重要性质,从而得到了线性空间一类新的度量刻画.  相似文献   

5.
6.
关于弱MCP空间与弱层空间   总被引:1,自引:0,他引:1  
本文引入了与已知的一些空间类非常类似的两个概念,我们分别称它们为弱MCP空间与弱层空间.本文主要讨论了这两空间类的等价命题与一些基本性质,及它们与原有空间类的关系.  相似文献   

7.
彭良雪 《数学杂志》2005,25(6):611-617
引入了两个很有联系的空间类JHB-空间与强J HB-空间,分别推广了J-空间与强J-空间.讨论了J-空间、强J-空间、J HB-空间及强JHB-空间类间的相包含关系及此四空间类逆包含的条件,还得到了JHB-空间的内部刻画,并证明了若对每个α∈S,Xα.都是非紧的连通空间,则积空间∏α∈S Xα是强J-空间。  相似文献   

8.
INTERPOLATION SPACES BETWEEN H^1 AND L^∞ ON SPACES OF HOMOGENEOUS TYPE   总被引:2,自引:0,他引:2  
Using the maximal function characterization of Hardy spaces,we study the interpolation spaces between H^1 and L^∞on spaces of homogeneous type.  相似文献   

9.
A.Pietsch^[1]在讨论核局部凸空间时给出了两类矢值序列空间l1[X]和l1{X}。本文建立了矢值序列空间l1[X]及l1{X}和连续线性算子空间L(c0,X)及绝对可和算子空间AS(c0,X)之间的拓扑同胚关系。通过c0上的矢值算子类L(c0,X)和AS(c0,X)及其上的拓扑等价关系,对局部凸空间X是核空间给出了一个新的特征刻划。  相似文献   

10.
本文证明了拓扑向量空间E是序列型空间的一个特征为:(1)E的每个序列开集都是开集;(2)取值于E中的任意无穷矩阵(xij)i,j,若对每个j均有limxij=xj,并且limxj=x,则一定存在严格递增序列(ik)和(jk)使得limxikjk=x.作为应用证明了序列型A-空间必是k-空间.  相似文献   

11.
We consider a spectral problem for a fourth-order ordinary differential equation with spectral parameter in a boundary condition. We study the structure of root spaces and analyze the basis properties in the space L p (0, l), 1 < p < ∞, of systems of root functions of that problem.  相似文献   

12.
In this paper we characterize the boundedness and compactness of weighted composition operators of H∞ into α-Bloch spaces on the unit ball in C^n.  相似文献   

13.
We point out that if the Hardy–Littlewood maximal operator is bounded on the space L p(t)(ℝ), 1 < ap(t) ≤ b < ∞, t ∈ ℝ, then the well-known characterization of the spaces L p (ℝ), 1 < p < ∞, by the Littlewood–Paley theory extends to the space L p(t)(ℝ). We show that, for n > 1 , the Littlewood–Paley operator is bounded on L p(t) (ℝ n ), 1 < ap(t) ≤ b < ∞, t ∈ ℝ n , if and only if p(t) = const. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 12, pp. 1709–1715, December, 2008.  相似文献   

14.
We study property (T) and the fixed-point property for actions on L p and other Banach spaces. We show that property (T) holds when L 2 is replaced by L p (and even a subspace/quotient of L p ), and that in fact it is independent of 1≤p<∞. We show that the fixed-point property for L p follows from property (T) when 1<p< 2+ε. For simple Lie groups and their lattices, we prove that the fixed-point property for L p holds for any 1< p<∞ if and only if the rank is at least two. Finally, we obtain a superrigidity result for actions of irreducible lattices in products of general groups on superreflexive spaces. Bader partially supported by ISF grant 100146; Furman partially supported by NSF grants DMS-0094245 and DMS-0604611; Gelander partially supported by NSF grant DMS-0404557 and BSF grant 2004010; Monod partially supported by FNS (CH) and NSF (US).  相似文献   

15.
Much of the recent literature on risk measures is concerned with essentially bounded risks in L . In this paper we investigate in detail continuity and representation properties of convex risk measures on L p spaces. This frame for risks is natural from the point of view of applications since risks are typically modelled by unbounded random variables. The various continuity properties of risk measures can be interpreted as robustness properties and are useful tools for approximations. As particular examples of risk measures on L p we discuss the expected shortfall and the shortfall risk. In the final part of the paper we consider the optimal risk allocation problem for L p risks.  相似文献   

16.
In this paper, we characterize, for 1≤p<∞, the multiple (p, 1)-summing multilinear operators on the product ofC(K) spaces in terms of their representing polymeasures. As consequences, we obtain a new characterization of (p, 1)-summing linear operators onC(K) in terms of their representing measures and a new multilinear characterization ofL spaces. We also solve a problem stated by M.S. Ramanujan and E. Schock, improve a result of H. P. Rosenthal and S. J. Szarek, and give new results about polymeasures. Both authors were partially supported by DGICYT grant BMF2001-1284.  相似文献   

17.
We compute the structure relations in special A -bialgebras whose operations are limited to those defining the underlying A -(co)algebra substructure. Such bialgebras appear as the homology of certain loop spaces. Whereas structure relations in general A -bialgebras depend upon the combinatorics of permutahedra, only Stasheff’s associahedra are required here. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 43, Topology and Its Applications, 2006.  相似文献   

18.
We study approximation of multivariate functions from a general separable reproducing kernel Hilbert space in the randomized setting with the error measured in the L norm. We consider algorithms that use standard information consisting of function values or general linear information consisting of arbitrary linear functionals. The power of standard or linear information is defined as, roughly speaking, the optimal rate of convergence of algorithms using n function values or linear functionals. We prove under certain assumptions that the power of standard information in the randomized setting is at least equal to the power of linear information in the worst case setting, and that the powers of linear and standard information in the randomized setting differ at most by 1/2. These assumptions are satisfied for spaces with weighted Korobov and Wiener reproducing kernels. For the Wiener case, the parameters in these assumptions are prohibitively large, and therefore we also present less restrictive assumptions and obtain other bounds on the power of standard information. Finally, we study tractability, which means that we want to guarantee that the errors depend at most polynomially on the number of variables and tend to zero polynomially in n −1 when n function values are used.  相似文献   

19.
We use microlocal and paradifferential techniques to obtain L 8 norm bounds for spectral clusters associated with elliptic second-order operators on two-dimensional manifolds with boundary. The result leads to optimal L q bounds, in the range 2⩽q⩽∞, for L 2 - normalized spectral clusters on bounded domains in the plane and, more generally, for two-dimensional compact manifolds with boundary. We also establish new sharp L q estimates in higher dimensions for a range of exponents q̅nq⩽∞. The authors were supported by the National Science Foundation, Grants DMS-0140499, DMS-0099642, and DMS-0354668.  相似文献   

20.
In this paper, we consider the global existence, uniqueness and L estimates of weak solutions to quasilinear parabolic equation of m-Laplacian type u t − div(|∇u| m−2u) = u|u| β−1Ω |u| α dx in Ω × (0,∞) with zero Dirichlet boundary condition in tdΩ. Further, we obtain the L estimate of the solution u(t) and ∇u(t) for t > 0 with the initial data u 0L q (Ω) (q > 1), and the case α + β < m − 1.  相似文献   

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