非参数回归函数之改良基于分割的估计的强相合性（英）

设(X,Y),(X1,Y1),…,(XnYn)为取值于 Rd× R的 i．i．d．随机变量,E(|Y|) ＜∞．设mn(x)为回归函数m(x)=E(|Y|X=x)基于分割的估计,本文在对mn(x)进行改良的条件下得到改良的基于分割的强相合估计．     

关于DMRL序的若干结论（英文）

设X,Y为非负绝对连续随机变量,X,Y分别具有各自的分布函数F_X,G_Y,使得F_X(0)=G_Y(0)=0,右连续的反函数F_X~(-1),G_Y~(-1),与生存函数F_X,G_Y.记X≤_(dmrl)Y,称X在DMRL(递减的平均剩余寿命)序下比Y小,如果函数∫_G_Y~(-1)(p)~∞G_Y(x)dx/∫_F_X~(-1)(p)~∞F_X(x)dx关于p∈(0,1)递增.考察了DMRL序的特征性质,获得了若干封闭与逆封闭性质.同时,给出了满足DMRL序的若干说明性实例.     

某些Banach空间的有限阶光滑点和强光滑点（英）

本文给出l_∞(X)以及L(l₁(X),Y),L(X,l_∞(Y))和L(X,c₀(Y))的单位球的有限阶光滑点和强光滑点的充要条件，这里X和Y都是任意的Banach空间.特别地，本文给出这些空间的单位球的光滑点和强光滑点的充要条件.     

乘积空间的k空间性质（Ⅱ）

证明集合论假设BF（ω2）下，如果X，Y都是具有素可数k网的正则空间，那么X×Y是k空间当且仅当空间对（X，Y）满足Tanaka条件．     

回归函数改良核估计的渐近分布

设(X1,Y1),…,(Xn,Yn)是来自二元总体(X,Y)的样本,若EY＜∞,则回归函数m(x)＝E(Y｜X＝x)存在。在本文中,考虑m(x)的改良核估计     

一类联图的距离谱半径以及盖理论（英文）

令X=(n₁,n₂,…,n_t),Y=(m₁,m₂,…,m_t)是两个t维递减序列.如果对所有的j,1≤j≤t,都有∑_i=1~j、n_i≥∑_i=1~j m_i以及∑_i=1~t n_i=∑_i=1~t m_i,则称X可盖Y,记作X■Y.如果X≠Y,则记作X■Y.本文考虑联图G(n₁,n₂,…,n_t;a)=(K_n1∪_n2∪…∪K_nt)∨K_a的谱半径,这里n₁+n₂+…+n_t+a=n,(n₁,n     

（0,2）型张量场诱导的线性变换的显表达式提取方法

对于黎曼流形（M,g）上（0,2）型光滑张量场R诱导出的线性变换R＊：X（M）→X（M）,其隐表达式为g（R＊（X）,Y）=S（X,Y）,X,Y∈X（M）,研究了从局部上提取出R＊（X）的显表达式的方法.提出一种所谓g正定提取方法,并将这种方法进一步应用到度量保形变换下的线性变换Φ＊（X）,L＊（X）.     

关于度量空间的开几乎s映像（英文）

Arhangel'skiǐ引入几乎s映射的概念:从拓扑空间X到拓扑空间Y上的映射f称为几乎s映射,若y是Y的非孤立点,则f~(-1)(y)是X的可分集.本文研究几乎s映射、近似s映射与边缘s映射之间的基本关系,得到了度量空间的开几乎s映像的内在刻画,并且讨论了度量空间上可数双商边缘s映射的性质.     

半群作用的稠密小周期集系统与完全传递系统（英文）

称一个动力系统(S,X)具有稠密g-小周期集,如果对任意非空开集UX,存在非空闭子集YU和S的一个g-syndetic子半群T,使得TYY;称一个传递的动力系统(S,X)是g-完全传递的,如果对S的每一个g-syndetic子半群T,(T,X)都是传递的.本文指出,每一个具有稠密g-小周期集的g-完全传递系统(S,X)不交于任何极小系统,其中S是一个可数交换半群,S最多只有可数个g-syndetic子半群且S中的每一个元S都为X到自身的满射.     

Γ-分布类的条件概率封闭性

X服从参数α和λ的Γ-分布,V与Y分别服从参数θ和λ的指数分布.我们证明了:在X＜Y的条件下,X的条件分布是参数α和θ+λ的Γ-分布;在X＜V＜X+Y的条件下,V的条件分布是参数α+1和θ+λ的Γ-分布.称此类性质为Γ-分布类的条件概率封闭性.对离散的负二项分布也证明了类似的结果.     

Universal non-compact operators between super-reflexive Banach spaces and the existence of a complemented copy of Hilbert space

Suppose that 1<p≦2, 2≦q<∞. The formal identity operatorI:l _p→l _qfactorizes through any given non-compact operator from ap-smooth Banach space into aq-convex Banach space. It follows that ifX is a 2-convex space andY is an infinite dimensional subspace ofX which is isomorphic to a Hilbert space, thenY contains an isomorphic copy ofl ₂ which is complemented inX.     

l p n Superspaces of spans of independent random variables

We show that for 1 ≦p < ∞,p ≠ 2, ifɛ > 0 is small enough andX ≦L _p is the span ofn independent Rademacher functions orn independent Gaussian random variables, then any superspaceY ofX satisfyingd(Y,L _p ^m ) ≦ 1 +ɛ has dimension larger thanr ⁿ, wherer =r(ɛ, p) > 1. This forms part of the author’s doctoral dissertation prepared at Texas A&M University under the direction of Professor W. B. Johnson. Supported in part by NSF DMS-85 00764.     

An extension of a result of ribe

It is proved that for every 1≦p<∞, 1≦q<∞ and for every sequence {p _n}, 1≦p _n<∞,p _n→p, the spaceX=(Σ⊕l _{p n}) _q (resp.U=(Σ⊕L _{p n}(0, 1)) _q ) is uniformly homeomorphic toX⊕l _p (resp.U⊕L _p(0, 1)). This extends Ribe’s result from the casep=1 to generalp<∞ and thus provides examples of uniformly convex, uniformly homeomorphic Banach spaces which are not Lipschitz equivalent.     

Denting and strongly extreme points in the unit ball of spaces of operators

For 1 ≤p ≤ ∞ we show that there are no denting points in the unit ball of ℓ(l^p). This extends a result recently proved by Grząślewicz and Scherwentke whenp = 2 [GS1]. We also show that for any Banach spaceX and for any measure space (Ω, A, μ), the unit ball of ℓ(L ¹ (μ), X) has denting points iffL ¹(μ) is finite dimensional and the unit ball ofX has a denting point. We also exhibit other classes of Banach spacesX andY for which the unit ball of ℓ(X, Y) has no denting points. When X* has the extreme point intersection property, we show that all ‘nice’ operators in the unit ball of ℓ(X, Y) are strongly extreme points.     

Embedding unconditional stable banach spaces into symmetric stable banach spaces

In this paper we prove the following result which solves a question raised by A. Pelczynski: “Every stable Banach space with an unconditional basis is isomorphic to a complemented subspace of some stable Banach space with a symmetric basis.” Moreover, we show that all the interpolation spacesl ^p ,l ^q _θ,X,1 1≦p, q<∞ andX stable, are stable.     

On complemented subspaces of the spaces (l p ) N ∩l q (l q )

Summary In this paper we study the complemented subspaces of the spaces (l^p)^N∩l^q(l^q), with 1≤p<q≤∞ or q=0, thereby showing that if (l^p)^N∩l^q(l^q)=F⊕G then either F or G contains a complemented copy of the whole space. Entrata in Redazione il 19 aprile 1999. Ricevuta versione finale il 4 febbraio 2000. Research supported by the Italian MURST.     

The bounds for matrices with monotonic rows

The bounds LX,Y (A) and ‖A‖ _X,Y of an operator A = (a _n,k ) _{n, k} ≥0 with monotonic rows are evaluated, where X and Y are quasi-normed real valued sequence spaces. In particular, in the case where X = ℓ _p and Y = ℓ _q , our results give the results when part 0 < p ≤ 1 and 0 < q < ∞ to complement the other results with range p ≥ 1 and 0 < q < ∞. Moreover, we give a partial answer to a problem [1, Problem 7.23] which was posed by Bennett.     

Recovery of band limited functions via cardinal splines

The main result of this paper asserts that if a function f is in the class B_π,p, 1 <p < ∞; that is, those p-integrable functions whose Fourier transforms are supported in the interval [ - π, π], then f and its derivatives f^(j) j = 1, 2, …, can be recovered from its sampling sequence{f(k)} via the cardinal interpolating spline of degree m in the metric ofL _q(ℝ)), 1 <p=q < ∞, or 11 <p=q < ⩽ ∞.     

Subspaces of<Emphasis Type="Italic">l</Emphasis><Superscript>∞</Superscript> (Γ) without quasicomplements

J. Lindenstrauss proves in [L] thatc ₀(Γ) is not quasicomplemented inl ^∞(Γ) while H. P. Rosenthal in [R] proves that subspaces, whose dual balls are weak* sequentially compact and weak* separable, are quasicomplemented inl ^∞(Γ). In this note it is proved that weak* separability of the dual is the precise condition determining whether a subspace, without isomorphic copies ofl ₁ and whose dual balls are weak* sequentially compact, is quasicomplemented or not inl ^∞(Γ). Especially spaces isomorphic tol _p(Γ), for 1<p<∞, have no quasicomplements inl ^∞(Γ) if Γ is uncountable.     

The weighted Herz-type Hardy spaces hK q α,p (ω1,ω2)

Let 1<q<∞, n(1−1/q)≤α<∞, 0<p<∞ and ω₁,ω₂ ɛA ₁(R ⁿ ) (the Muckenhoupt class). In this paper, the author introduce the weighted Herz-type Hardy spaces hk _q ^α,p (gw₁,ω₂) and present their atomic decomposition. Using the atomic decomposition, the author find out their dual spaces, establish the boundedness on these spaces of the pseudo-differential operators of order zero and show thatD(R ⁿ ), the class of C^∞(Rⁿ)-functions with compactly support, is dense inhK _q ^α,p (ω₁,ω₂) and there is a subsequence, which converges in distrbutional sense to some distribution ofhK _q ^α,p (ω₁,ω₂), of any bounded sequence inhK _q ^α,p (ω₁,ω₂). In addition, the author also set up the boundedness of some non-linear quantities in compensated compactness. Supported by the NECF and the NECF and the NNSF of China.