On the absolute matrix summability of Fourier series and some associated series

The object of the paper is to study the absolute matrix summability problem of Fourier series, conjugate series and some associated series under a new set of conditions on matrix methods, generalising many known results in the literature.     

UNIFORM CONVERGENCE OF CESARO MEANS OF NEGATIVE ORDER OF DOUBLE TRIGONOMETRIC FOURIER SERIES

In this paper we prove that iff ∈ C([-π,π]2) and the function f is bounded partial p-variation for some p ∈ [1, ∞), then the double trigonometric Fourier series of a function f is uniformly (C;-α,-β) summable (α β＜ 1/p,α,β＞ 0) in the sense of Pringsheim. If α β≥ 1/p, then there exists a continuous function f0 of bounded partial double trigonometric Fourier series of fo diverge over cubes.     

Cesàro Transforms of Fourier Coefficients of -functions

In this note, we show that Cesàro transforms of Fourier cosine or sine coefficients of any -function are Fourier cosine or sine coefficients of some -function.

     

球上Zygmund 型空间上的加权Cesàro 算子

该文在Cⁿ中单位球上讨论了Zygmund 型空间(小Zygmund 型空间)之间的加权Cesàro 算子T_g 的有界性和紧性特征, 得到了以下的结果: (1) T_g 是Z^p 到Z^q的有界算子或紧算子的充要条件; (2) T_g 是 Z^p₀ 到Z^q₀ 的有界算子或紧算子的充要条件.     

Iterating the Cesàro operators

The discrete Cesàro operator associates to a given complex sequence the sequence , where . When is a convergent sequence we show that converges under the sup-norm if, and only if, . For its adjoint operator , we establish that converges for any .

The continuous Cesàro operator, , has two versions: the finite range case is defined for and the infinite range case for . In the first situation, when is continuous we prove that converges under the sup-norm to the constant function . In the second situation, when is a continuous function having a limit at infinity, we prove that converges under the sup-norm if, and only if, .

     

Summability factor relations between absolute weighted and Cesàro means

By , we denote the set of all sequences such that Σ?_na_n is summable V whenever Σa_n is summable U, where U and V are two summability methods. Recently, Sar?göl has characterized the set for k > 1,α > ?1 and arbitrary positive sequences Now, in the present paper, we characterize the sets , k > 1 and , k ≥ 1 for arbitrary positive sequences Hence we extend these results to the range α≥ ? 1. In this way, some open problems in this topic are also completed.     

过渡金属表面有机官能团硅烷膜的研究——镍电极表面γ-氨丙基三甲氧基硅烷膜的结构

在镍电极表面制备了γ-氨丙基三甲摒在硅烷膜并对其形成和结构进行了研究 。镍电极表面有机官能团硅烷膜的X射线光电子能谱（XPS）结果表明氮、硅等元素 在电极表面的存在，并且氨基在膜中有若干种存在方式，包括自由氨基和质子化的 氨基。通过对表面增强拉曼散射光谱（SERS）谱图的分析，发现与电极表面作用的 吸附基团硅醇羟基和氨基发生了竞争吸附，它们及其邻近基团的拉曼谱几随着电位 的负称除了相对强度发生变化以外，还发生了一定的位移，这缘于吸咐基团吸附的 量和吸附取向随电极电位发生了变化并形成的更为复杂的界面结构；氨基不同存在 方式之间也会随之发生转变，这一结果与X射线光电子能谱分析的结果相符合。原 子力显微镜（AFM）结果表明镍电极表面的有机官能团硅烷膜呈现为一种较规则的 多孔结构。     

Divergent Cesàro and Riesz means of Jacobi and Laguerre expansions

We show that for below certain critical indices there are functions whose Jacobi or Laguerre expansions have almost everywhere divergent Cesàro and Riesz means of order .

     

On Cesàro Means of Double Trigonometric Fourier Series

Zhizhiashvili studied questions associated with the approximation properties of Cesàro means of trigonometric Fourier series for functions of two variables in the spaces H. It is proved here that the corresponding estimate cannot be improved for p = 1 or p = .     

关于Neuman-Sándor平均的一些特殊组合不等式

研究了Neuman-Sándor平均NS(a,b)关于调和平均H(a,b)、算术平均A(a,b)、二次平均Q(a,b)若干特殊组合的序关系,给出最佳参数α₁,α₂,α₃,α₁₄,β₁,β₂,β₃,β₄∈(0,1),使得下列双向不等式：$\sqrt{a_{1}Q^{2}(a,b)+(1-a_{1})A^{2}(a,b)}< NS(a,b)<\sqrt{\beta_{1}Q^{2}(a,b)+(1-\beta_{1})A^{2}(a,b),}\\ \sqrt{[a_{2}Q(a,b)+(1-a_{2})A(a,b)]A(a,b)}< NS(a,b)<\sqrt{[\beta_{2}Q(a,b)+(1-\beta_{2})A(a,b)]A(a,b),}\\ \sqrt{a_{e}Q^{2}(a,b)+(1-a_{3})H^{2}(a,b)}< NS(a,b)<\sqrt{\beta_{3}Q^{2}(a,b)+(1-\beta_{3})H^{2}(a,b),}\\ \sqrt{[a_{4}Q(a,b)+(1-a_{4})H(a,b)]A(a,b)}< NS(a,b)<\sqrt{[\beta_{4}Q(a,b)+(1-\beta_{4})H(a,b)]A(a,b),}$对所有不同的正实数a和b均成立。