Sharp affine Trudinger–Moser inequalities: A new argument

We set up the sharp Trudinger–Moser inequality under arbitrary norms. Using this result and the $L_{p}$ Busemann-Petty centroid inequality, we will provide a new proof to the sharp affine Trudinger–Moser inequalities without using the well-known affine Pólya–Szegö inequality.

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Bibliographic Details
Published inCanadian mathematical bulletin Vol. 64; no. 4; pp. 765 - 778
Main Authors Duy, Nguyen Tuan, Lam, Nguyen, Long Le, Phi
Format Journal Article
LanguageEnglish
Published Canada Canadian Mathematical Society 01.12.2021
Cambridge University Press
Subjects
Centroids
Inequalities
Inequality
Norms
affine energy
46E35
Trudinger–Moser inequality
Lp Busemann–Petty centroid inequality
35A23
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Summary:We set up the sharp Trudinger–Moser inequality under arbitrary norms. Using this result and the $L_{p}$ Busemann-Petty centroid inequality, we will provide a new proof to the sharp affine Trudinger–Moser inequalities without using the well-known affine Pólya–Szegö inequality.
ISSN:0008-4395
1496-4287
DOI:10.4153/S0008439520000806