, Volume 34, Issue 1, pp 1-12
Date: 16 Apr 2010

Note on Affine Gagliardo–Nirenberg Inequalities

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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 Pólya–Szegö principle.