Note on Affine Gagliardo-nirenberg Inequalities
نویسنده
چکیده
This note proves sharp affine Gagliardo-Nirenberg inequalities which are stronger than all known sharp Euclidean Gagliardo-Nirenberg inequalities and imply the affine L−Sobolev inequalities. The logarithmic version of affine L−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 Pólys-Szegö principle.
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