Orlicz空间中三角多项式倒数对周期可微函数的逼近定理

利用Orlicz空间内有关不等式技巧在Orlicz空间内研究了用三角多项式的倒数逼近周期可微函数的问题.得到了一个逼近定理及其推论.     

插值三角多项式在Orlicz空间逼近的渐进等式

对于具有等距分布插值结点的三角多项式,借助广义的Minkowski不等式在Orlicz空间内建立了由三角多项式逼近的渐近等式.并对于Orlicz空间内不同的函数类给出不同的结果.     

A Note on Pad ′e Approximants Pairs as Limits of Algebraic Polynomials Pairs of Weighted Best Approximation in Orlicz Spaces

In this short note, we show the behavior in Orlicz spaces of best approxima-tions by algebraic polynomials pairs on union of neighborhoods, when the measure of them tends to zero.     

A Note on Pad Approximants Pairs as Limits of Algebraic Polynomials Pairs of Weighted Best Approximation in Orlicz Spaces

In this short note, we show the behavior in Orlicz spaces of best approximations by algebraic polynomials pairs on union of neighborhoods, when the measure of them tends to zero.     

Polynomials and identities on real Banach spaces

We study the duality theory for real polynomials and functions on Banach spaces. Our approach leads to a unified treatment and generalization of some classical results on linear identities and polynomial characterizations due to Fréchet, Mazur, Orlicz, Reznick, Wilson, and others.     

On approximation by reciprocals of polynomials with positive coefficients in Orlicz spaces

This paper discusses the approximation by reciprocals of polynomials with positive coefficients in Orlicz spaces and proved that if f(x) ∈ LM*[0,1], changes its sign at most once in (0,1), then there exists x0 ∈ (0,1) and a polynomial Pn ∈ Πn(+) such that f (x) -Pn (x)x-x0 M ≤ Cω( f,n-1/2 )M, where Πn(+) indicates the set of all polynomials of degree n with positive coefficients.     

On Approximation by Reciprocals of Polynomials with Positive Coefficients

In order to study the approximation by reciprocals of polynomials with real coefficients, one always assumes that the approximated function has a fixed sign on the given interval. Sometimes, the approximated function is permitted to have finite sign changes, such as $l(l\geq1)$ times. Zhou Songping has studied the case $l=1$ and $l\geq2$ in $L^{p}$ spaces in order of priority. In this paper, we studied the case $l\geq2$ in Orlicz spaces by using the function extend, modified Jackson kernel, Hardy-Littlewood maximal function, Cauchy-Schwarz inequality, and obtained the Jackson type estimation.     

Orlicz Brunn-Minkowski理论

本文主要介绍Orlicz Brunn-Minkowski理论,并从下面3个方面介绍该理论:Orlicz投影体和Orlicz质心体、Orlicz加法与其相关体积不等式、Orlicz Minkowski问题.     

赋Orlicz范数的Orlicz—Lorentz空间的严格凸性

本文对于赋Ｌｕｘｅｍｂｕｒｇ范数的Ｏｒｌｉｃｚ－Ｌｏｒｅｎｔｚ空间     

On the convexity coefficient of Musielak–Orlicz function spaces equipped with the Orlicz norm

In Hudzik and Landes, the convexity coefficient of Musielak–Orlicz function spaces over a non-atomic measure space equipped with the Luxemburg norm is computed whenever the Musielak–Orlicz functions are strictly convex see [6]. In this paper, we extend this result to the case of Musielak–Orlicz spaces equipped with the Orlicz norm. Also, a characterization of uniformly convex Musielak–Orlicz function spaces as well as k-uniformly convex Musielak–Orlicz spaces equipped with the Orlicz norm is given.     

关于Orlicz凸体的收敛性的注(英文)

本文研究了Orlicz投影体和Orlicz质心体的性质.利用几何分析的方法,获得了Orlicz投影算子和Orlicz质心算子的连续性.     

赋Orlicz范数的Orlicz序列空间的接近一致凸性

本文给出了赋Ｏｒｌｉｃｚ序列空间的Ｈ点的充分必要条件,进而得至了赋Ｏｒｌｉｃｚ范数的Ｏｒｌｉｃｚ序列空间具有（Ｈ）性质的判据．同时给出了赋Ｏｒｌｉｃｚ范数的Ｏｒｌｉｃｚ序列空间的一致ＵＫＫ和接近一致凸性的等价条件。     

A direct approach to Orlicz–Sobolev capacity

This paper is motivated by Federer and Ziemer's potential-free approach to Sobolev capacity. We extend their results to Orlicz–Sobolev spaces and analyze the resulting notion of Orlicz–Sobolev capacity. In particular, we explore the relationship between the Orlicz–Sobolev capacity of a set and its Hausdorff dimension and then establish the quasicontinuity of Orlicz–Sobolev functions.     

Uniform Gateaux differentiability and weak uniform rotundity of Musielak–Orlicz function spaces

Criteria for uniform Gateaux differentiability and weak uniform rotundity of Musielak–Orlicz function spaces equipped with the Orlicz norm as well as the Luxemburg norm are presented. Interpretations of the criteria in the case of Orlicz spaces are given. It is worth noticing that criteria for the Luxemburg norm are different than for the Orlicz norm.     

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。     

Orlicz mixed quermassintegrals Dedicated to Professor Ren De-lin on the Occasion of his 80th Birthday

The notion of mixed quermassintegrals in the classical Brunn-Minkowski theory is extended to that of Orlicz mixed quermassintegrals in the Orlicz Brunn-Minkowski theory. The analogs of the classical CauchyKubota formula, the Minkowski isoperimetric inequality and the Brunn-Minkowski inequality are established for this new Orlicz mixed quermassintegrals.     

椭球的Orlicz质心体(英文)

主要研究了Lutwak等所引入的Orlicz质心体(Lutwak E,Yang D,Zhang G.Orliczcentroid bodies.J.Differential Geom.,2010,84:365-387).利用Orlicz质心体在线性变换下的不变性,证明了椭球的Orlicz质心体仍是椭球.作为例子,计算了当取两个特定的凸函数时单位球的Orlicz质心体的支持函数.     

Orlicz mixed quermassintegrals

The notion of mixed quermassintegrals in the classical Brunn-Minkowski theory is extended to that of Orlicz mixed quermassintegrals in the Orlicz Brunn-Minkowski theory. The analogs of the classical Cauchy-Kubota formula, the Minkowski isoperimetric inequality and the Brunn-Minkowski inequality are established for this new Orlicz mixed quermassintegrals.     

Orlicz混合相交体

本文研究了Orlicz混合相交体及其性质.利用几何分析方法提出了Orlicz混合相交体的概念,获得了Orlicz混合相交体算子的连续性和仿射不变性.通过积分方法和Steiner对称,建立了Orlicz混合相交体的仿射等周不等式.