GEOMETRIC PROPERTIES OF BANACH SPACE VALUED BOCHNER-LEBESGUE SPACES WITH VARIABLE EXPONENT

被引：11

作者：

Cheng, Chen ^{[1
]}

Xu, Jingshi ^{[2
]}

机构：

[1] Liuzhou Railway Vocat Tech Coll, Liuzhou 545007, Peoples R China

[2] Hainan Normal Univ, Dept Math, Haikou 571158, Peoples R China

来源：

JOURNAL OF MATHEMATICAL INEQUALITIES | 2013年 / 7卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Variable exponent; Bochner-Lebesgue space; Radon-Nikodym property; reflexivity; uniformly convexity; 2-MICROLOCAL BESOV; DECOMPOSITION; SMOOTHNESS; EQUATIONS;

D O I：

10.7153/jmi-07-41

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the Banach space valued Bochner-Lebesgue spaces with variable exponent are introduced. Then the dual space, the reflexivity, uniformly convexity and uniformly smoothness of these new spaces are obtained. Finally the properties of the Banach valued Bochner-Sobolev spaces with variable exponent are also given. Those are a generalization of scalar valued Lebesgue and Sobolev spaces with variable exponent.

引用

页码：461 / 475

页数：15

共 16 条

[1] Almeida A, 2008, GEORGIAN MATH J, V15, P195
[2] Besov spaces with variable smoothness and integrability
Almeida, Alexandre
Hasto, Peter
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2010, 258 (05) : 1628 - 1655
[3] Amann H., 1995, Linear and Quasilinear Parabolic Problems. Vol. I. Abstract Linear Theory,, V89
[4] [Anonymous], 1977, AM MATH SOC
[5] Function spaces of variable smoothness and integrability
Diening, L.
Hasto, P.
Roudenko, S.
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2009, 256 (06) : 1731 - 1768
[6] Lebesgue and Sobolev Spaces with Variable Exponents
Diening, Lars
Harjulehto, Petteri
Hasto, Peter
Ruzicka, Michael
[J]. LEBESGUE AND SOBOLEV SPACES WITH VARIABLE EXPONENTS, 2011, 2017 : 1 - +
[7] Overview of differential equations with non-standard growth
Harjulehto, Petteri
Hasto, Peter
Le, Ut V.
Nuortio, Matti
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (12) : 4551 - 4574
[8] Hästö PA, 2009, MATH RES LETT, V16, P263
[9] Kakutani S., 1938, Thoku Math. J, V45, P188
[10] Atomic, molecular and wavelet decomposition of generalized 2-microlocal Besov spaces
Kempka, Henning
[J]. JOURNAL OF FUNCTION SPACES AND APPLICATIONS, 2010, 8 (02): : 129 - 165

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