Refined Sobolev Inequalities in Lorentz Spaces

被引：8

作者：

Bahouri, Hajer ^{[2
]}

Cohen, Albert ^{[1
,3
]}

机构：

[1] UPMC Univ Paris 06, Lab Jacques Louis Lions, UMR 7598, F-75005 Paris, France

[2] Univ Paris 11, Ctr Math, Fac Sci & Technol, F-94010 Creteil, France

[3] CNRS, Lab Jacques Louis Lions, UMR 7598, F-75005 Paris, France

来源：

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2011年 / 17卷 / 04期

关键词：

Refined Sobolev inequalities; Refined Hardy inequalities; Lorentz spaces; Besov spaces;

D O I：

10.1007/s00041-011-9171-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish refined Sobolev inequalities between the Lorentz spaces and homogeneous Besov spaces. The sharpness of these inequalities is illustrated on several examples, in particular based on non-uniformly oscillating functions known as chirps. These results are also used to derive refined Hardy inequalities.

引用

页码：662 / 673

页数：12

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