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Equivalence of Sharp Trudinger-Moser Inequalities in Lorentz-Sobolev Spaces

  • Hanli TangEmail author
Article
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Abstract

The critical and subcritical Trudinger-Moser inequalities in Lorentz Sobolev space have been studied by Cassani and Tarsi (Asymptot. Anal. 64(1-2):29–51, 2009), Lu and Tang (Adv. Nonlinear Stud. 16(3):581–601, 2016). In this paper, we will prove that these critical and subcritical Trudinger-Moser inequalities are actually equivalent and thus extend those equivalence results of Lam et al. (Rev. Mat. Iberoam 33(4):1219–1246, 2017) into Lorentz Sobolev spaces.

Keywords

Critical Trudinger-Moser inequality Subcritical Trudinger-Moser inequalities Lorentz-Sobolev spaces Equivalence 

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Notes

Acknowledgments

The author wishes to thank the referees very much for their very careful reading and many useful comments and suggestions on the improvement of the exposition of the paper.

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesBeijing Normal UniversityBeijingChina

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