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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Open Access
Creators
  1. Jeffrey S. Case
License In Copyright (Rights Reserved)
Work Type Article
Publisher
  1. World Scientific Pub Co Pte Lt
Publication Date March 11, 2020
Publisher Identifier (DOI)
  1. 10.1142/s0219199720500157
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  1. Communications in Contemporary Mathematics
Deposited September 09, 2021

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