On Hardy-Type Inequalities and Hankel Transforms

 For the real Hardy spaces , we shall show the Hardy type integral inequalities, and applying the inequalities we shall establish the Hardy’s inequalities with respect to Hankel transforms. Received 21 October 1997; in revised form 19 October 1998     

Weighted Vector Valued Inequalities for Generalized Singular Integral Operators on Spaces of Homogeneous Type

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The Boas Problem on Hankel Transforms

Journal of Fourier Analysis and Applications - Norm equivalences between a function and its Hankel transform are studied both in the context of weighted Lebesgue spaces with power weights, and in...     

Convolution Hankel Transforms on the Zemanian Spaces

In this paper we investigate the convolution Hankel transforms on the Zemanian spaces of Hankel transformable functions and distributions. The convolution Hankel transform is defined on generalized functions by using the adjoint method. Our new definition includes as special cases other known definitions of the convolution Hankel transform of distributions. Finally we establish a distributional inversion formula for the transformation under consideration involving Bessel differential operators.     

Some Representations of Translations of the Product of Two Functions for Hankel Transforms and Jacobi Transforms

By introducing a series of operators T_y^(m), m = 0,1,. . . , a representation of the generalized translation of the product of two functions associated to Hankel transforms is given. These operators have certain properties of finite differences. The analogous problem related to Jacobi transforms is also studied.     

平方函数的加权及向量值不等式

证明一类带粗糙核平方函数的加权及l~r-向量值不等式,其中所用的权函数为径向权.作为推论,我们得出了带H~1-核的Marcinkiewicz积分μ_Ω的相应不等式.     

向量值奇异积分算子的交换子

本文分别讨 论了 Ｈａｒｄｙ Ｌｉｔｔｌｅｗ ｏｏｄ 极大 算子和奇 异积分算 子的交换 子在加权 Ｈｅｒｚ 空间 ,加权 Ｌｐ空间中的 有界性     

Lp Contraction Semigroups for Vector Valued Functions

Let be a contraction semigroup on the space of vector valued functions ( is a Hilbert space). In order to study the extension of to a contaction semigroup on , Shigekawa [Sh] studied recently the domination property where is a symmetric sub-Markovian semigroup on . He gives in the setting of square field operators sufficient conditions for the above inequality. The aim of the present paper is to show that the methods of [12] and [13] can be applied in the present setting and provide two ways for the extension of to We give necessary and sufficient conditions in terms of sesquilinear forms for the contractivity property as well as for the above domination property in a more general situation.     

Banach空间上重排函数不等式

本文利用重排函数不等式,证明了几个鞅不等式,这些不等式包含R.L.Long^[1]的结果,可以用来刻划Banadh空间的性质。     

Salzer定理的二元向量形式

本文将在切触有理插值中起重要作用的Salzer定理推广到了多元向量的情形.     

Approximation of Vector Valued Functions

In this paper, we extend the well-known result of Lipschitz approximation of lower semi-continuous functions to a class of lattice valued vector functions. We then use this approximation to get convergence results and we give two applications to the law of large numbers and to an ergodic theorem.     

Third-Order Hankel Determinant for Transforms of the Reciprocal of Bounded Turning Functions

Mathematical Notes - In this paper, we make an attempt to introduce a new subclass of analytic functions. Using the Toeplitz determinants, we obtain the best possible upper bound for the...     

二元对角向量值有理插值的算法

首先提出了二元对角向量值有理插值问题,它包括主对角和副对角两种向量值有理插值,并分别给出了主对角线和副对角线上向量值有理插值的两种算法,即直接求系数bi,j的算法和基于Samelson广义逆所定义的特殊初等变换的矩阵算法.然后构造了在预给极点情况下求主对角线和副对角线上向量值有理插值的矩阵算法.最后给出多个数值例子说明上述算法的有效性.     

Weak Compactness Criteria for Set Valued Integrals and Radon Nikodym Theorem for Vector Valued Multimeasures

Some criteria for weak compactness of set valued integrals are given. Also we show some applications to the study of multimeasures on Banach spaces with the Radon-Nikodym property.     

Vector Variational Inequalities for Nondifferentiable Convex Vector Optimization Problems

In this paper, we consider a nondifferentiable convex vector optimization problem (VP), and formulate several kinds of vector variational inequalities with subdifferentials. Here we examine relations among solution sets of such vector variational inequalities and (VP). Mathematics Subject classification (2000). 90C25, 90C29, 65K10 This work was supported by the Brain Korea 21Project in 2003. The authors wish to express their appreciation to the anonymous referee for giving valuable comments.     

Ratio Mercerian Theorems with Applications to Hankel and Fourier Transforms

We complete and complement our recent work on Drasin-Shea-Jordantheorems for Fourier and Hankel transforms. In improving onthe methods of our previous work, we were led to certain ratioMercerian theorems for general kernels; these yield definitiveversions of our earlier results for Fourier and Hankel transforms.1991 Mathematics Subject Classification: primary 44A15; secondary47B38.     

Vector Valued Martingale-Ergodic and Ergodic-Martingale Theorems

We prove martingale-ergodic and ergodic-martingale theorems for vector-valued Bochner integrable functions. We obtain dominant and maximal inequalities. We also prove weighted and multiparameter martingale-ergodic and ergodic-martingale theorems.