Abstract
We derive the sharp Moser–Trudinger–Onofri inequalities on the standard n-sphere and CR \((2n+1)\)-sphere as the limit of the sharp fractional Sobolev inequalities for all \(n\ge 1\). On the 2-sphere and 4-sphere, this was established recently by Chang and Wang. Our proof uses an alternative and elementary argument.
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Acknowledgements
The author is grateful to Professor G. Tian for his kind advice on presentation and for his insightful comments. He also thanks Professor R. Frank for clarifying the limiting process in the literature.
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This work was supported in part by NSFC 11501034, NSFC 11571019 and the key project NSFC 11631002.
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Xiong, J. A Derivation of the Sharp Moser–Trudinger–Onofri Inequalities from the Fractional Sobolev Inequalities. Peking Math J 1, 221–229 (2018). https://doi.org/10.1007/s42543-019-00012-3
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DOI: https://doi.org/10.1007/s42543-019-00012-3