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

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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.

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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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  1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Hanli Tang

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  1. Hanli Tang
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Correspondence to Hanli Tang.

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The research of the author is supported by National Natural Science Foundation of China (Grant No. 11701032) and China Postdoctoral Science Foundation (Grant No. 2015M570959).

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Tang, H. Equivalence of Sharp Trudinger-Moser Inequalities in Lorentz-Sobolev Spaces. Potential Anal 53, 297–314 (2020). https://doi.org/10.1007/s11118-019-09769-9

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