加权的Szász-Kantorovich-Bézier算子在Orlicz空间中的逼近等价定理（英文）

本文介绍了由Young函数生成的Orlicz空间L_Φ~*[0,∞),然后建立了修正的加权K-泛函与加权光滑模的等价定理,并利用它得到了加Jacobi权的Szász-Kantorovich-Bézier算子在Orlicz空间中逼近的正、逆和等价定理.     

修正的积分型求和算子在Orlicz空间中的逼近（英文）

本文介绍由Φ(x)构成的Orlicz空间L_Φ~*[0,∞),并介绍Orlicz空间的Hardy-Littlewood性质.然后给出Orlicz空间中修正的加权K-泛函与加权连续模的等价定理,最后建立修正的积分型求和算子在Orlicz空间中逼近的正、逆定理和等价定理.从而推广了该算在L_p[0,∞)空间中逼近性质.     

Bernstein-Kantorovi多项式在奥尔里奇空间中的逼近

设M(u)为N函数,L_(M[a,b]~*为对应之闭区间[a,b]上的奥尔里奇空间。对f(x)∈L_(M[a,b]~*,我们定义正整数阶的积分光滑模为     

Ba空间中的多元加权光滑模与Bernstein Durrmeyer算子

该文引进Ba空间多元加权光滑模,推广L^p空间的DitzianTotik模, 证明该模与K泛函的等价性. 作为应用,讨论定义在单纯形上多元Bernstein-Durrmeyer算子与多元加权光滑模之间的关系. 即以多元加权光滑模为尺度, 建立Bernstein-Durrmeyer算子在Ba空间逼近阶的上界与下界估计.     

Orlicz空间内第一类不适定积分方程的解

讨论由L~2[a,b]到Orlicz空间L_M~*[a,b]内第一类积分方程 integral from n=a to b(K(x,y)g(y)dy=f(x)) (1)f∈L_M~*[a,b]。这里K(x,y)满足 integral from n=a to b integral from n=a to b(|K(x,y)|~2dxdy〈∞) L_M~*[a,b]为N函数M(u)生成的Orlicz空间,并赋以Orlicz范数||·||_M;L_(N)~*[a,b]为M(u)的余N函数N(v)生成的Orlicz空间,赋以Luxemburg范数。     

加权复合算子在两类函数空间之间的序有界性北大核心CSCD

本文首先研究了加权复合算子W_(Φ,φ)(f):=Φfoφ的Hilbert-Schmidt性质与序有界性的对应关系.接着利用加权Dirichlet空间D^(q)_(β)(0相似文献   

关于空間L_(MΦ)和D_Φ~h(Ⅲ)——L_(MΦ)与D_Φ~h的等价性

作者在[1],[2]中引进了空間D_Φ~h并且进行了若干討論。本文的目的是証明空間L_(MΦ),L_(MΦ)~*,L_(MΦ)~(**)相应的与空間D_Φ~h,(D_Φ~h)~*,(D_Φ~h)~(**)等价,然后利用这些結果来給出[1],[2]的部分定理的一种新証明,并且在定条件下还可以得到空間D_Φ~h上的有界綫性泛函的一般表达式。 設μ为在点集△的子集E的σ环(?)上的完全,可数可加測度(μ完全指的是:从μ(E)=0,F(?)E可推出F∈(?))并且μ(△)=∞;又設h(x)是定义在△上的无界μ可測函数而且μ(△_n)<∞,其中△_n={x∈△‖h(x)|≤n}(n=1,2,…)。     

定常Navier-Stokes方程有限元分析

的近似解.方程(1.1)中的Γ是区域Ω(R~N)的边界.假设Γ充分光滑,在适当条件下,上述问题的解(u,p)(∈(H_0~1)(Ω))~N×L_0~2(Ω))是存在唯一的.关于H_0~1(Ω),L_0~2(Ω)等记号将在下面统一说明.Falk曾用Galerkin-Langrange乘子法找Stokes问题的近似解,近似解空间(V_(1h)~0)~N×X_h取为(H_0~1(Ω))~N×L~2(Ω)的有限维子空间.[3]中指出,当Ω不是多角形区域时,构造H_0~1(Ω)且满足一定条件的有限维子空间V_(1h)~0是比较复杂     

Baskakov算子加Jacobi权逼近及其导数的正逆定理

本文利用加权光滑模ω_~2λ(f,t)ω给出了Baskakov算子加Jacobi权逼近的正逆定理;另外,研究了加权下Baskakov算子导数与所逼近函数光滑性之间的关系.     

发展方程Galerkin解法的敛速估计

本文考虑了发展方程的半离散及离散情况下Galerkin解的误差估计,其中A=L_1 L_2,L_1是V椭圆的(见[8]),L_1~(-1)L_2是希氏空间V中的全连续算子。对于问题(1)的半离散的Galerkin逼近给出了L~(V)—和L~2(H)—模估计。对于离散时间的Galerkin逼近给出了L~2(H)—模估计。     

可数簇全拟-Φ-渐近非扩张映象和广义混合平衡问题以及极大单调算子的收缩投影迭代算法

先介绍全拟-φ-渐近非扩张映象的概念,然后在具有Kadec—Klee性质的一致光滑、严格凸的Banach空间的框架下,利用混合收缩投影的迭代算法,用以寻求广义混合平衡问题的解集GMEP,可数簇全拟-φ-渐近非扩张映象的不动点集(?)F(S_(i))和极大单调算子的零点集T~(-1)0的公共元.在适当的条件下,证明了逼近于这一公共元的强收敛定理.推广和改进了一些最新结果.     

鞅的双权双&Phi|-函数极大不等式

该文研究了鞅Orlicz空间加权不等式, 主要包括弱(Φ₁,Φ₂) -型加权不等式和强(Φ₁,Φ₂) -型加权不等式. 讨论了这些不等式成立的充分必要条件.     

Copies of c0(Г) and ?∞(Г)/c0(Г) in quotients of Banach spaces with applications to Orlicz and Marcinkiewicz spaces

Let X be a Banach space, let Y be its subspace, and let Г be an infinite set. We study the consequences of the assumption that an operator T embeds ?_221E;(Г) into X isomorphically with T(c₀(Г)) ⊂ Y. Under additional assumptions on T we prove the existence of isomorphic copies of c₀(Г^ℵ0) in X/Y, and complemented copies ?_∞(Г) in X/Y. In concrete cases we obtain a new information about the structure of X/Y. In particular, L∞[O,1]/C[O,1] contains a complemented copy of ?_∞/c₀, and some natural (lattice) quotients of real Orlicz and Marcinkiewicz spaces contain lattice-isometric and positively I-complemented copies of(real) ?_∞/c₀.     

Orlicz spaces without extreme points

Orlicz function and sequence spaces unit balls of which have no extreme points are completely characterized for both (the Orlicz and the Luxemburg) norms. Their subspaces of order continuous elements, with the norms induced from the whole Orlicz spaces without extreme points in their unit balls are also characterized. The well-known spaces L₁ and c₀ with unit balls without extreme points are covered by our results. Moreover, a new example of a Banach space without extreme points in its unit ball is given (see Example 1). This is the subspace a(L₁+L_∞) of order continuous elements of the space L₁+L_∞ equipped with the norm whenever 0<a<∞ and μ(T)>1/a.     

Banach Spaces with Property (M) and their Szlenk Indices

We show that a separable Banach space with property (M*) has a Szlenk index equal to ω₀, and a norm with an optimal modulus of asymptotic uniform smoothness. From this we derive a condition on the Szlenk functions of the space and its dual which characterizes embeddability into c ₀ or an ℓ _p -sum of finite dimensional spaces. We also prove that two Lipschitz-isomorphic Orlicz sequence spaces contain the same ℓ _p -spaces.      

Calderón--Lozanovskii; construction for mixed norm spaces

We show that the Calderón--Lozanovskii; construction φ(.) commutes with arbitrary mixed norm spaces, that is, φ(E₀[F₀], E₁[F₁]) = φ(E₀, E₁) [φ(F₀, F₁)] if and only if φ is equivalent to a power function. This result we obtain by giving characterizations of the corresponding embeddings of φ(E₀[F₀], E₁[F₁]) into φ₀ (E₀, E₁)[φ₁ (F₀, F₁)] and vice versa in terms of the functions φ, φ₀, φ₁. As a particular case, we get embeddings of an Orlicz space with mixed norms into an Orlicz space on a product of measure spaces. Applications to classical operators between mixed norm Orlicz spaces are also discussed. This revised version was published online in June 2006 with corrections to the Cover Date.     

二阶常微分方程无穷多点边值问题的正解

该文运用锥上的不动点定理研究非线性二阶常微分方程无穷多点边值问题 u'+a (t ) f (u)=0, t∈(0, 1), u(0)=0, u(1)=∑^∞_{i =1}α _i u ( ξ _i ) 正解的存在性. 其中ξ _i∈ (0,1),α _i∈ [0,∞), 且满足∑^∞_i=1α_iξ _i <1.α∈C([0,1], [0,)),f∈C ([0,∞), [0,∞)).     

On the upper bounds of WCS coefficients in Orlicz function spaces

Abstract  Let Φ(u) be an N-function and let and be the Orlicz function spaces equipped with the gauge norm and the Orlicz norm respectively. The author refines some results on the upper bounds of the weak convergent sequence coefficients and given in [8] and [7, Ch.3.2]. Theorems 1 and 2 are given in Section 2. Several examples, given in Section 3, are used to make comments upon the papers of Yan [11], [12] and [13]. Keywords Orlicz space, WCS coefficient and normal structure coefficient Mathematics Subject Classification (2000) 46B30     

Some properties of functions in Orlicz space

For functions in Orlicz space L _M ^* , we study the behavior of (t)dt, where x^* (t) is non-increasing and equimeasurable with ¦ x(t) ¦. We establish the existence of unbounded functions in L _M ^* that are not limits of bounded functions and for which . Moreover, we establish a new criterion for an N-function to belong to the class ₂ and a sufficiency test for a function to belong to Orlicz space.Translated from Matematicheskie Zametki, Vol. 3, No. 2, pp. 145–156, February, 1968.