Weak compactness in

We characterize weak compactness and weak conditional compactness of subsets of in terms of regular methods of summability. We also study when these results still hold using only convergence in the sense of Cesàro.

     

Summability of Fourier orthogonal series for Jacobi weight functions on the simplex in

We study the Fourier expansion of a function in orthogonal polynomial series with respect to the weight functions

on the standard simplex in . It is proved that such an expansion is uniformly summable on the simplex for any continuous function if and only if . Moreover, it is shown that means define a positive linear polynomial identity, and the index is sharp in the sense that means are not positive for .

     

Iterates of a product of conditional expectation operators

Let (Ω,F,μ) be a probability space and let T=P₁P₂?Pd be a finite product of conditional expectations with respect to the sub σ-algebras F₁,F₂,…,Fd. We show that for every f∈Lp(μ), 1<p?2, the sequence {Tnf} converges μ-a.e., with

     

On a Difference Matrix and Its Properties

In the present paper, a new difference matrix via difference operator D is introduced. Let x =(xk) be a sequence of real numbers, then the difference operator D is defined by D(x)n= ∑nk=0(-1)k(n n-k)xk, where n = 0, 1, 2, 3, ···. Several interesting properties of the new operator D are discussed.     

修饰基团的结构对 β -环糊精衍生物的分析特性的影响Ⅰ 可离解基团的影响

本文以螯合阳离子、螯合阴离子和具有阴、阳电性互变异构体的三种类型的显色体系为例 ,比较研究了未经修饰的 β -环糊精 (β-CD)与经荷阴离子、阳离子取代基修饰的 β-CD衍生物对这三种类型显色体系的增效作用的机理 ,总结出这些衍生物对显色反应作用的规律 .     

Tauberian type gap conditions for Cesàro summation methods

In this paper, we study gap conditions ensuring, for the class of series satisfying them, that the Cesàro methods (C, k) and (C, α) with fixedk and α (0<k<α) are equivalent. We obtain a sufficient condition in which gaps of the corresponding sizes separate uniformly bounded sets ofk+1 nonzero elements rather than neighboring nonzero elements (as in the classical case ofk=0). Translated fromMatematicheskie Zametki, Vol. 65, No. 1, pp. 118–129, January, 1999.     

Bounds of weighted multilinear Hardy-Cesàro operators in p-adic functional spaces

We introduce the p-adic weighted multilinear Hardy-Cesàro operator. We also obtain the necessary and sufficient conditions on weight functions to ensure the boundedness of that operator on the product of Lebesgue spaces, Morrey spaces, and central bounded mean oscillation spaces. In each case, we obtain the corresponding operator norms. We also characterize the good weights for the boundedness of the commutator of weighted multilinear Hardy-Cesàro operator on the product of central Morrey spaces with symbols in central bounded mean oscillation spaces.     

单位球上$\mu$-Bloch空间之间的广义Ces\`{a}ro算子

Let μ, v ∈ [0, 1） be normal functions and g be holomorphic function on the unit ball. In this paper, we prove that the generalized Cesaro operator Tg ：βμ→βv is bounded and compact.     

Generalized Cesàro operators,fractional finite differences and Gamma functions

In this paper, we present a complete spectral research of generalized Cesàro operators on Sobolev–Lebesgue sequence spaces. The main idea is to subordinate such operators to suitable $C_0$-semigroups on these sequence spaces. We introduce that family of sequence spaces using the fractional finite differences and we prove some structural properties similar to classical Lebesgue sequence spaces. In order to show the main results about fractional finite differences, we state equalities involving sums of quotients of Euler's Gamma functions. Finally, we display some graphical representations of the spectra of generalized Cesàro operators.     

Ratio limit theorems and Tauberian theorems for vector-valued functions and sequences

We prove ratio limit theorems for (C,γ)-means (γ?0) and Abel means of functions and sequences in Banach spaces, and ratio Tauberian theorems for (C,γ)-means (γ?1) and Abel means of functions and sequences in Banach lattices.