Note on Affine Gagliardo–Nirenberg Inequalities

被引：0
|
作者：
Zhichun Zhai
机构：
[1] University of Alberta,Department of Mathematical and Statistical Science
来源：
Potential Analysis | 2011年 / 34卷
关键词：
Sobolev spaces; Gagliardo–Nirenberg inequalities; Sharp constant; Rearrangements; Pólya–Szegö principle; Primary 46E35; 46E30;
D O I：
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摘要：
This note proves sharp affine Gagliardo–Nirenberg inequalities which are stronger than all known sharp Euclidean Gagliardo–Nirenberg inequalities and imply the affine Lp-Sobolev inequalities. The logarithmic version of affine Lp-Sobolev inequalities is verified. Moreover, an alternative proof of the affine Moser–Trudinger and Morrey–Sobolev inequalities is given. The main tools are the equimeasurability of rearrangements and the strengthened version of the classical Pólya–Szegö principle.
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页码：1 / 12
页数：11
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