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Sharp affine Trudinger–Moser inequalities: A new argument

Part of: Partial differential equations Linear function spaces and their duals

Published online by Cambridge University Press:  22 October 2020

Nguyen Tuan Duy ,
Nguyen Lam  and
Phi Long Le
Nguyen Tuan Duy
Affiliation:
Faculty of Economics and Law, University of Finance-Marketing, 2/4 Tran Xuan Soan St., Tan Thuan Tay Ward, Dist. 7, HCM City, Vietname-mail:nguyenduy@ufm.edu.vn
Nguyen Lam
Affiliation:
School of Science and the Environment, Grenfell Campus, Memorial University of Newfoundland, Corner Brook, NL A2H 5G4, Canadae-mail:nlam@grenfell.mun.ca
Phi Long Le*
Affiliation:
Institute of Research and Development, Duy Tan University, Da Nang550000, Vietnam
*
e-mail:lelongphi@duytan.edu.vn
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Abstract

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.

Keywords

Lp Busemann–Petty centroid inequalityaffine energyTrudinger–Moser inequality

MSC classification

Primary: 46E35: Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
Secondary: 35A23: Inequalities involving derivatives and differential and integral operators, inequalities for integrals
Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 4 , December 2021 , pp. 765 - 778
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Copyright
© Canadian Mathematical Society 2020

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Footnotes

P.L.L. is corresponding author.

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