Note on Affine Gagliardo-Nirenberg Inequalities

作者：Zhai Zhichun^*

来源：Potential Analysis, 2011, 34(1): 1-12.

DOI：10.1007/s11118-010-9176-y

• Sobolev spaces
• Gagliardo-Nirenberg inequalities
• Sharp constant
• Rearrangements
• Polya-Szego principle

This note proves sharp affine Gagliardo-Nirenberg inequalities which are stronger than all known sharp Euclidean Gagliardo-Nirenberg inequalities and imply the affine L-p-Sobolev inequalities. The logarithmic version of affine L-p-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 Polya-Szego principle.

• 出版日期2011-1