Orlicz-Pettis Type Theorems via Strong p-Cesàro Convergence

We obtain a new version of the Orlicz-Pettis theorem within the frame of the strong p-Cesàro convergence.     

Factorization of Cesàro and Hilbert matrices based on generalized Cesàro matrix

ABSTRACT

In this paper, we introduce factorizations for the Hilbert and Cesàro matrices based on generalized Cesàro matrix and as the application, we generalize the Hardy's inequality versus Hilbert's.     

Some inclusion theorems for absolute summability

In this work the inclusion relations between absolute summability domains of a normal matrix A and certain factorable matrices are described. Thus, some classes of factorable matrices transforming the absolute summability domain of A into a set of convergent or absolutely convergent series are characterized. As an application, the special case where A is the Cesàro matrix is considered.     

自共轭常微分算子特征值的一种基于分离特征参数的数值解法

该文发现了特征方程 ly(x, λ) = λy(x, λ) 一般解的一种关于特征参数λ 的幂级数表示及其求解方法, 借此给出了自共轭常微分算子特征值的一种新的数值解法, 并给出了算法的稳定性分析和误差估计. 最后, 通过数值实例来说明该算法是有效的.     

A Komlós Theorem for abstract Banach lattices of measurable functions

Consider a Banach function space X(μ) of (classes of) locally integrable functions over a σ-finite measure space (Ω,Σ,μ) with the weak σ-Fatou property. Day and Lennard (2010) [9] proved that the theorem of Komlós on convergence of Cesàro sums in L¹[0,1] holds also in these spaces; i.e. for every bounded sequence n(fn) in X(μ), there exists a subsequence k(fnk) and a function f∈X(μ) such that for any further subsequence j(hj) of k(fnk), the series converges μ-a.e. to f. In this paper we generalize this result to a more general class of Banach spaces of classes of measurable functions — spaces L¹(ν) of integrable functions with respect to a vector measure ν on a δ-ring — and explore to which point the Fatou property and the Komlós property are equivalent. In particular we prove that this always holds for ideals of spaces L¹(ν) with the weak σ-Fatou property, and provide an example of a Banach lattice of measurable functions that is Fatou but do not satisfy the Komlós Theorem.     

Extended Cesàro Operators between Different Bergman

In this paper, we obtain the characterizations onμ for (p, q) - φ Carleson measure,different weighted Bergman spaces as some application.     

B~α空间和Q_K空间之间的加权Cesro算子

讨论了B~α空间和Q_K空间之间的加权Cesro算子T_g的有界性,给出了B~α空间到Q_K空间的加权Cesro算子T_g有界的充要条件.另外也给出了Q_K空间到B~α空间的加权Cesro算子T_g有界的充要条件.