Boundeness of a Class of Maximal Operators on H~p Spaces on Compact Lie Groups

In this paper we discuss the weak type(H^p,L^p) boundedness of a class of maximal operators T*^ψ and themaximal strong mean boundedness of a family of the operators ｛T^ψ｝ on the atomic H^p spaces on compact Lic groups.Also,we obtain the correspoding convergent results.     

Musielak—Orlicz空间L^p（x）（Ω）的若干凸性

本文研究了一类特殊的Musielak-Orlicz空间Lp(x)(Ω)赋予Luxemburg范数时的严格凸性,局部一致凸性,弱局部一致凸性,中点局部一致凸性与一致凸性.利用Banach空间几何学中刻画凸性的一般方法,并结合一般Musielak-Orlicz空间凸性的判别准则,获得了用p(x)刻画空间Lp(x)(Ω)赋予Luxemburg范数时,上述几种凸性的充分必要条件.     

Existence of Generalized Heteroclinic Solutions of the Coupled Schr¨odinger System under a Small Perturbation

The following coupled Schrodinger system with a small perturbation
is considered, where β and ε are small parameters. The whole system has a periodic solution with the aid of a Fourier series expansion technique, and its dominant system has a heteroclinic solution. Then adjusting some appropriate constants and applying the fixed point theorem and the perturbation method yield that this heteroclinic solution deforms to a heteroclinic solution exponentially approaching the obtained periodic solution （called the generalized heteroclinic solution thereafter）.     

About Compact and Sequentially Compact Coincide in Topological Groups with the Axiom （A1）

This paper is concerned with the relation between the compactness and sequential compactness in a topological space or a topological group, and show that the compactness and sequential compactness coincide in a topolpgical group with the axiom (A1).     

Perturbations of Moore–Penrose Metric Generalized Inverses of Linear Operators in Banach Spaces

In this paper,the perturbations of the Moore–Penrose metric generalized inverses of linear operators in Banach spaces are described.The Moore–Penrose metric generalized inverse is homogeneous and nonlinear in general,and the proofs of our results are different from linear generalized inverses.By using the quasi-additivity of Moore–Penrose metric generalized inverse and the theorem of generalized orthogonal decomposition,we show some error estimates of perturbations for the singlevalued Moore–Penrose metric generalized inverses of bounded linear operators.Furthermore,by means of the continuity of the metric projection operator and the quasi-additivity of Moore–Penrose metric generalized inverse,an expression for Moore–Penrose metric generalized inverse is given.     

B（E,F）中光滑Banach子流形B＊（E,F）

令E和F是Banach空间;B（E,F）,B^＋（E,F）,Φ（E,F）,SΦ（E,F）和R（E,F）分别表示映E到F的有界线性、双裂、Fredholm、半Fredholm和有限秩算子全体.令∑表示下列集合之一：{T∈Φ（E,F）：IndexT=constant和dimN（T）=constant},{T∈SΦ（E,F）：dimN（T）=constant＆lt;∞或codimR（T）=constant＆lt;∞之一成立}和{T∈R（E,F）：RankT=constant＆lt;∞},下面是已知的：∑是B（E,F）中的光滑子流形,且切空间T_A∑={B∈B（E,F）：BN（A） R（A）,（？）A∈∑}.然而,B^＊（E,F）={T∈B^＋（E,F）：dimN（T）=codimR（T）=∞},失去特征数dimN（A）,codimR（A）,index（A）和Rank（A）,寻找它的一个子类组成B（E,F）中的光滑子流形,这是很困难的.幸运地,我们发现B^＊（E,F）就是B（E,F）的一个光滑子流形,且在每一点A∈B^＊（E,F）它的切空间T_AB^＊（E,F）={T∈B（E,F）：TN（A） R（A）}.这样,B^＋（E,F）的几何结构被给出,亦即,B＋（E,F）是以上互不相交的诸光滑子流形的并．同时我们对任一A∈B＋（E,F）,给出了一个装配在一个固定的Banach空间上,通过A的光滑子流形s（A）．为了这些,许多广义逆扰动分析的结果被推广．特别地,在E：F：Rn情况下,我们得到：Rank（A）=r〈n,的奇异n×n矩阵全体∑r是B（R^n）的一个道路连通的光滑子流形且有维数dime∑r=2nr-r^2．这样,B（R^n）除熟知的代数和分析结构外,又有了一个像B^＋（E,F）一样的几何结构．     

Quantitative Shisha—Mond Type Theorem of Probability Expression of （C0） Semigroups of Operators

In this paper we set up quanttative shisha-Mond type theorem of probability expression of (C0)-semigroup of opertors and we give an example by introducing S-λ probability distribution to ob-tain corresponding quantitative estimation.     

Approximation Theorems of Bernstein-Durrmeyer Operators in L_M~（Ba） Spaces

With the weighted modulus of smoothness as a metric,we prove the direct and the inverse theorems of approximation by Bernstein-Durrmeyer operators in LBa M spaces. Especially an approximation equivalent theorem of the operators is also obtained.     

The Approximation Properties of Certain Interpolation Operators of Entire Exponential Type（1）

In this paper, the authers introduce certain entire exponential type interpolation operatots and study the convergence problem of these operatots in c(R) or Lp(R) (1≤p<∞)     

Energy Equality and Uniqueness of Weak Solutions to MHD Equations in L∞（0, T; L^n（Ω））

In this paper, we study the energy equality and the uniqueness of weak solutions to the MHD equations in the critical space L∞（0, T; L^n（Ω）. We prove that if the velocity u belongs to the critical space L∞（0, T; L^n（Ω）, the energy equality holds. On the basis of the energy equality, we further prove that the weak solution to the MHD equations is unique.     

Ideals in the Roe Algebras of Discrete Metric Spaces with Coefficients in B（H）

The notion of an ideal family of weighted subspaces of a discrete metric space X with bounded geometry is introduced. It is shown that, if X has Yu＇s property A, the ideal structure of the Roe algebra of X with coefficients in B（H） is completely characterized by the ideal families of weighted subspaces of X, where B（H） denotes the C＊-algebra of bounded linear operators on a separable Hilbert space H.     

A Characterization of ＊-Automorphism on B（H）

Let H be a Hilbert space and A be a standard ＊-subalgebra of B（H）. We show that a bijective map Ф ： A →A preserves the Lie-skew product AB - BA＊ if and only if there is a unitary or conjugate unitary operator U ∈A（H） such that Ф（A） = UAU＊ for all A ∈ A, that is, Фis a linear ＊ -isomorphism or a conjugate linear ＊-isomorphism.     

Local Spectral Properties of Total Class wF（p, r, q） Operators

In this paper, by initiative research on local spectral theory of total class wF(p, r, q) operators, we get some important results. Such as total class wF(p, r,q) op-erators is normaloid operator, the local spectral subspace of total class wF(p, r, q) operators is equal to the space EλH(Eλ the Reisz idempotent, with respect to ,λ, of T), total class wF(p, r, q) operators has finite ascent, and so on.     

Matching Realization of Uq（sln＋1） of Higher Rank in the Quantum Weyl Algebra Wq（2n）

In the paper, we further realize the higher rank quantized universal enveloping algebra Uq（sln＋1） as certain quantum differential operators in the quantum Weyl algebra Wq （2n） defined over the quantum divided power algebra Sq（n） of rank n. We give the quantum differential operators realization for both the simple root vectors and the non-simple root vectors of Uq（sln＋1）. The nice behavior of the quantum root vectors formulas under the action of the Lusztig symmetries once again indicates that our realization model is naturally matched.     

An Upper Bound of Essential Norm of Composition Operator on H2 （Bn）

The authors give an upper bound of the essential norm of a composition operator on H ²(B _n ), which involves the counting function in the higher dimensional value distribution theory defined by S. S. Chern. A criterion is also given to assure that the composition operator on H ²( _Bn ) is bounded or compact.     

The Dichotomy Between Traces on d-sets F in R^n and the Density of D（R^n／Г） in Function Spaces

A space Apq^s （R^n） with A ： B or A = F and s ∈R, 0 〈 p, q 〈 ∞ either has a trace in Lp（Г）, where Г is a compact d-set in R^n with 0 〈 d 〈 n, or D（R^n／Г） is dense in it. Related dichotomy numbers are introduced and calculated.     

On uniqueness of （fuzzy） relation in some generalized rough set model

In rough set theory, crisp and/or fuzzy binary relations play an important role in both constructive and axiomatic considerations of various generalized rough sets. This paper considers the uniqueness problem of the （fuzzy） relation in some generalized rough set model. Our results show that by using the axiomatic approach, the （fuzzy） relation determined by （fuzzy） approximation operators is unique in some （fuzzy） double-universe model.