
The Frank–Lieb approach to sharp Sobolev inequalities
<jats:p> Frank and Lieb gave a new, rearrangement-free, proof of the sharp Hardy–Littlewood–Sobolev inequalities by exploiting their conformal covariance. Using this they gave new proofs of sharp Sobolev inequalities for the embeddings [Formula: see text]. We show that their argument gives a direct proof of the latter inequalities without passing through Hardy–Littlewood–Sobolev inequalities, and, moreover, a new proof of a sharp fully nonlinear Sobolev inequality involving the [Formula: see text]-curvature. Our argument relies on nice commutator identities deduced using the Fefferman–Graham ambient metric. /jats:p
Electronic version of an article published as 'Communications in Contemporary Mathematics', 23, 03, 2020, 2050015 10.1142/s0219199720500157 © World Scientific Publishing Company https://doi.org/10.1142/s0219199720500157
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Work Title | The Frank–Lieb approach to sharp Sobolev inequalities |
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License | In Copyright (Rights Reserved) |
Work Type | Article |
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Publication Date | March 11, 2020 |
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Deposited | September 09, 2021 |
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