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Note on affine Gagliardo-Nirenberg inequalities.

Mon, 08/17/2009 - 18:30 — SomNambul
Authors: Zhichun Zhai
Subjects: Functional Analysis
link: http://arxiv.org/abs/0908.2095
Abstract

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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