Orlicz范数下的Hardy-Hilbert不等式

给出了Orlicz范数下的Hardy-Hilbert不等式的一种形式,建立了当N-函数M(u)及其余N-函数N(u)均满足Δ′条件时Orlicz范数下的积分型及双级数型Hardy-Hilbert不等式.  

时间测度上具有Holling-N类功能反应和扩散的捕食系统的周期解

在时间测度上研究了一类具有Holling-N类功能反应和扩散的捕食系统,利用Mawhin重合度理论建立了这类系统周期解存在的一些新的充分性判据,从而使这一类系统的连续与离散情形,即相应的微分方程和差分方程的周期解存在性问题得到了统一.  

On a Pair of Geometric Parameters of Orlicz Norm

Let be a pair of complementary N--funCtions, where gh and op are the right deriVatives of. andW respectively Defineandas in Wull1. Clearly, 1 5 Q. 5 oo for every .(u). Wangl'j and Wu, Chen and Wangl']showed that. E V2(0) if and only if Q. < oo and. E A2(0) if and ouly if q. > l. for andRenl4] utilized the parameter Q. when they Offered the fonwig esthoation of KOttmanconstants of the Orlicz sequence space l. equlpped with Orlicz norm:whereChen showed that (see [5, p.211)wherefor and …  

Level sets of a typical function

We determine the level set structure of a typical function.

  

Integral Representations and Transforms of N-Functions. I

The author has proposed a new approach to extrapolation of operators from the scale of Lebesgue spaces to the Orlicz spaces beyond this scale. In this article comprising two parts we develop some mathematical method that enables us to prove extrapolation theorems for arbitrary behavior of an operator in the Lebesgue scale (i.e., in the case when the norm of the operator is an arbitrary function of p) and also in the case when the basic scale is an interval of the Lebesgue scale with exponents separated from 1 or +∞. In this event, we face ill-posed problems of inversion of the classical Mellin and Laplace type integral transforms over nonanalytic functions in terms of their asymptotic behavior on the real axis and also the question about the properties of convolution type integral transforms on classes of N-functions. In the first part of the article we study integral representations for N-functions by expansions in power functions with a positive weight and the behavior of convolution type integral transforms on classes of N-functions.  

Integral representations and transforms of N-functions. II

We study the problem of reconstruction of a convolution type integral transform from its behavior for power functions. We solve some of the problems posed in Part I of the article.  

齐型空间上的Orlicz Morrey空间极大算子有界性

In this paper, the characterization of boundedness of Hardy-Littlewood maximal operators in Orlicz-Morrey spaces L^Фψ（X,μ） of homogeneous type is founded.  

关于T.J.Rivlin的一个问题

本文在连续函数空间内按两种范数‖·‖_Ｍ（Ｏｒｌｉｃｚ范数）和‖·‖_(Ｍ)（Ｌｕｘｅｍｂｕｒｇ范数分别解决了Ｔ．Ｊ．Ｒｉｖｌｉｎ的一个问题  

关于Orlicz序列空间的包含关系

设Φ，Ψ为一对互余的Ｎ－函数，本文给出了包含关系成立的充要条件，并修正Ｃｈｅｎ［１，ｐ，１６８］的一个例子.  

Orlicz型序列空间的暴露性

对赋Luxember范数或Orlicz范数的Orlicz型序列空间，诸如古典的、广义的及参数式的，本文总结、补充、比较列出了暴露点及暴露性的充分必要刻画，并对以往结果中的错误进行了修正，从而在序列空间方面系统地完成了有关暴露性的刻画。