Note on affine Gagliardo-Nirenberg inequalities

Details Note on affine Gagliardo-Nirenberg inequalities Note on affine Gagliardo-Nirenberg inequalities

2009-08-14

arxiv.org/abs/0908.2095v1

Mathematics

Functional Analysis

10 pages

Scientific paper

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 P\'{o}lys-Szeg\"{o} principle.

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