Sharp Marchaud and converse inequalities in Orlicz spaces

For spaces on , and , sharp versions of the classical Marchaud inequality are known. These results are extended here to Orlicz spaces (on , and ) for which is convex for some , , where is the Orlicz function. Sharp converse inequalities for such spaces are deduced.

     

Generalized absolute Cesaro summability of a Fourier series

In an attempt to study the scope of a theorem due to Pati, the authors have established that φ(t) logK|t∈B _u V in (0,π)⟹ΣA _n (x) is |C, 0,β| forβ>1, at the pointt = x.     

Walsh—Fourier级数在p—级数域上的Hardy空间和Herz空间中的Cesaro可和性

讨论了二维Walsh-Fourier级数在p－级数域的整环上的两个函数空间Hardy空间和Herz空间中的Cesaro可和性。     

级数的常规可和，Cesàro可和与Abel可和的几点讨论

讨论级数常规可和、Cesaro可和与Abel可和的关系．利用数学分析级数理论,证明Abel可和适用范围最广,Cesaro可和其次,级数常规可和适用范围最小．这个结论丰富了经典级数理论,为实际应用中选用合适可和提供依据．     

Multipliers for the absolute euler summability of fourier series

In this paper, the author has investigated necessary and sufficient conditions for the absolute Euler summability of the Fourier series with miltipliers. These conditions are weaker than those obtained earlier by some workers. It is further shown that the multipliers are best possible in certain sense.     

Summability of Product Jacobi Expansions

Orthogonal expansions in product Jacobi polynomials with respect to the weight function W_α, β(x)=∏^d_j=1 (1−x_j)^α_j (1+x_j)^β_j on [−1, 1]^d are studied. For α_j, β_j>−1 and α_j+β_j−1, the Cesàro (C, δ) means of the product Jacobi expansion converge in the norm of L^p(W_{α, β}, [−1, 1]^d), 1p<∞, and C([−1, 1]^d) if

Full-size image

Moreover, for α_j, β_j−1/2, the (C, δ) means define a positive linear operator if and only if δ∑^d_i=1 (α_i+β_i)+3d−1.     

Absolute Summability Factors and Absolute Tauberian Theorems for Double Series and Sequences

Let A and B be the linear methods of the summability of double series with fields of bounded summability MA _b ^' and B _b ^' , respectively. Let T be certain set of double series. The condition x T is called B _b-Tauberian for A if A _b ^' B _b ^' .Some theorems about summability factors enable one to find new B _b-Tauberian conditions for A from the already known B _b-Tauberian conditions for A.     

Cesaro Summability with Respect to Two-Parameter Walsh Systems

 The one- and two-parameter Walsh system will be considered in the Paley as well as in the Kaczmarz rearrangement. We show that in the two-dimensional case the restricted maximal operator of the Walsh–Kaczmarz (C, 1)-means is bounded from the diagonal Hardy space H ^p to L ^p for every . To this end we consider the maximal operator T of a sequence of summations and show that the p-quasi-locality of T implies the same statement for its two-dimensional version T _α. Moreover, we prove that the assumption is essential. Applying known results on interpolation we get the boundedness of T _α as mapping from some Hardy–Lorentz spaces to Lorentz spaces. Furthermore, by standard arguments it will be shown that the usual two-parameter maximal operators of the (C, 1)-means are bounded from L ^p spaces to L ^p if . As a consequence, the a.e. convergence of the (C, 1)-means will be obtained for functions such that their hybrid maximal function is integrable. Of course, our theorems from the two-dimensional case can be extended to higher dimension in a simple way. (Received 20 April 2000; in revised form 25 September 2000)     

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.     

Bergman型空间的Cesaro算子

设g1．g2为正规函数．对所有的0〈p．q〈∞,我们得到了Bergma型空间的加权Cesaro算子Tψ：Ag1^p→Ag2^q为有界算子和紧算子的充要条件．     

On the Floquet problem for second-order Marchaud differential systems

Solutions in a given set of the Floquet boundary value problem are investigated for second-order Marchaud systems. The methods used involve a fixed point index technique developed by ourselves earlier with a bound sets approach. Since the related bounding (Liapunov-like) functions are strictly localized on the boundaries of parameter sets of candidate solutions, some trajectories are allowed to escape from these sets. The main existence and localization theorem is illustrated by two examples for periodic and anti-periodic problems.     

ON LACUNARY STATISTICAL CONVERGENCE OF ORDER α

In this article, we introduce the concept of lacunary statistical convergence of order α of real number sequences and give some inclusion relations between the sets of lacunary statistical convergence of order α and strong Nαθ(p)-summability. Furthermore, some relations between the spaces Nαθ(p) and Sαθare examined.     

Summability matrices and sequences of 0's and 1's

Summary Conditions are given on a nonnegative regular summability matrix A to ensure that for a given number α, 0 ≤ α ≤ 1, there exists a sequence x consisting of 0's and 1's such that Ax converges to α.     

Spherical Summability and a Vector-Valued Inequality

We prove a vector-valued weak type (1, 1) inequality for theBochner-Riesz means of the critical order.     

一类迭代序列Cesaro平均收敛的条件

该文给出了帐篷映射产生的迭代序列Cesaro平均收敛的条件．研究了它与实数二进展式度量性质之间的联系．     

单位球上Bergman空间到Besov空间的广义Cesaro算子(英文)

本文利用Carleson测度刻画了Bergman空间到Besov空间的广义Cesaro算子T_g的有界性和紧性,同时得到了(p,q)-φCarleson测度的一些性质.     

m重非齐次马氏链的Cesaro平均收敛性

引入m重非齐次马氏链的Cesaro平均收敛的概念,给出并证明m重非齐次马氏链的一个Cesaro平均收敛定理.作为应用,得到了m重非齐次马氏链熵率存在的一个定理.     

两两独立同分布序列Cesàro强大数定律的收敛速度

设{X,Xn,n≥0}是两两独立同分布的随机变量序列,11．为了证明这一结论而获得到的两两负相关随机变量序列的Cesaro强大数定律收敛速度的结果本身也是有意义的．此结果对于同分布的两两NQD序列也是对的．     

n-球面上的Cesàro算子的带权强性求和

设1(n-1)/p-n/2，f∈L^p(Ω_n)，σ^δ_N(f)(x)表示f(x)在n-球面Ω_n上的Cesàro平均.本文证明了(?)a_k≤A（A是绝对常数），这个结果加强了现有的结论.     

关于可列非齐次马氏链Cesaro平均收敛性及二元函数的强大数定律

该文的目的是要研究可列非齐次马氏链的Cesaro平均收敛性及二元函数的强大数定律.并利用这两者研究可列非齐次马氏链的Shannon-Mcmillan定理.