Orlicz-Bochner序列空间中的局部一致非l_n~((1))与非l_n~((1))性质（英文）

本文得到在赋Luxemburg范数及Orlicz范数下Orlicz-Bochner序列空间l_M(X_s)具有局部一致非l_n~((1))性质或非l_n~((1))性质的充要条件,据此即得l_M(X_s)具有局部一致非方性或非方性的判据.     

关于赋范线性空间非方性的定义

James与Schffer分别对赋范线性空间引入两种不同的(一致、局部一致)非方性的定义。本文证得两种(一致)非方性的定义等价,而两种局部一致非方性全然不同,并对有限非原子测度的赋Orlicz范数的Orlicz空间给出James意义局部一致非方性的判据。     

Orlicz空间的非方性质

本文讨论Orlicz空间关于Luxemburg 范数的非方性,得到这类空间一致非方、局部一致非方和在一点一致非方的简明判别准则。     

Orlicz-Sobolev空间的弱局部一致凸性

本文研究了Orlicz-Sobolev空间的弱局部一致凸性.通过运用Orlicz空间和Sobolev空间的技巧,得到了赋Luxemburg范数的Orlicz-Sobolev空间具有弱局部一致凸性的充要条件和赋Orlicz范数的Orlicz-Sobolev空间具有弱局部一致凸性的充分条件.     

Orlicz空间的若干紧一致凸性和k-drop凸性

给出赋Luxemburg范数的Orlicz函数空间的紧一致凸、弱紧一致凸、紧局部一致凸、弱紧局部一致凸和k-drop凸的判据,并且据此得到在Orlicz函数空间中这些凸性的等价关系.     

Orlicz-Sobolev空间的中点局部一致凸性

本文研究了Orlicz-Sobolev空间的中点局部一致凸性，通过结合Orlicz空间和Sobolev空间的技巧得到分别赋Luxemburg范数和赋Orlicz范数的Orlicz-Sobolev空间具有中点局部一致凸性的充要条件．     

具有弱正规结构的Orlicz空间

W.Kirk给出了弱正规结构（WNS）的概念,并证明了弱正规结构（WNS）蕴涵弱不动点性质,B.Sims给出了具有（k)性质的巴拿赫空间,并证明了（k)性质蕴函弱正规结构,陈述涛给出了伪－k(pseudo-(k))性质及弱各向一致凸（WURED）的概念,推广了B.Sims的结果,并讨论了Orlicz序列空间是弱各向一致凸的充要条件,本利用实变函数理论及赋范线性空间中有关知识,给出Orlicz函空间是弱各向一致凸的充分必要条件,所得以的结论和证明方法与序列空间情形都有实质不同。     

广义Orlicz序列空间的非方性

研究了广义Orlicz序列空间关于Luxemburg范数的非方性,参考经典Orlicz空间的讨论方法,发展了广义情形下的新方法,给出了判别该性质的充要条件.     

Musielak-Orlicz空间的复局部一致凸

引进复局部一致凸和复局部一致凸点的概念 ,并在Musielak Orlicz空间中给出二者的充分必要判别条件     

Musielak-Orlicz序列空间的一致Gateaux可微性

利用Musielak-Orlicz函数列的某些性质,给出了赋Luxemburg范数的Musielak-Orlicz序列空间是有一致Gateaux可微性的充要条件及赋Orlicz范数的Musielak-Orlicz序列空间是弱一致凸的判别准则.     

The locally uniformly non‐square points of Orlicz–Bochner sequence spaces

In this paper, we investigate the locally uniformly non‐square point of Orlicz–Bochner sequence spaces endowed with Luxemburg norm. Analysing and combining the generating function M and properties of the real Banach space X , we get sufficient and necessary conditions of locally uniformly non‐square point, which contributes to criteria for locally uniform non‐squareness in Orlicz–Bochner sequence spaces. The results generalize the corresponding results in the classical Orlicz sequence spaces.     

Sharp generalized Trudinger inequalities via truncation

We prove that the generalized Trudinger inequalities into exponential and double exponential Orlicz spaces improve to inequalities on Orlicz-Lorentz spaces provided they are stable under truncation.     

Orlicz序列空间的一致单调系数及应用

本文给出了Ｏｒｌｉｃｚ序列空间一致单调系数数值，同时给出了Ｏｒｌｉｃｚ序列空间具有一致单调性的条件，进而讨论具有一致单调性的Ｏｒｌｉｃｚ序列空间中的最佳逼近算子的一些特征。     

A note on geometrical properties of Banach spaces using ψ-direct sums

Let X be a Banach space and ψ a continuous convex function on [0,1] satisfying certain conditions. Let Xψ_⊕X be the ψ-direct sum of X. In this note, we characterize the strict convexity, uniform convexity and uniformly non-squareness of Banach spaces using ψ-direct sums, which extends the well-known characterization of these spaces.     

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。     

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.     

Uniform nonsquareness and locally uniform nonsquareness in Orlicz–Bochner function spaces and applications

In this paper, criteria for uniform nonsquareness and locally uniform nonsquareness of Orlicz–Bochner function spaces equipped with the Orlicz norm are given. Although, criteria for uniform nonsquareness and locally uniform nonsquareness in Orlicz function spaces were known, we can easily deduce them from our main results. Moreover, we give a sufficient condition for an Orlicz–Bochner function space to have the fixed point property.     

Uniformly non-1 n /(1) Orlicz spaces

A characterisation of uniformly non-1 _n ^/(1) Orlicz space is obtained intrinsically in terms of the Young function determining the Orlicz space. It is shown that a uniformally non-1 _n ^/(1) Orlicz space is reflexive. This work was supported in part by Air Force Grant G2A-152015.