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Fractional Sobolev and Hardy-Littlewood-Sobolev inequalities

Abstract : This work focuses on an improved fractional Sobolev inequality with a remainder term involving the Hardy-Littlewood-Sobolev inequality which has been proved recently. By extending a recent result on the standard Laplacian to the fractional case, we offer a new, simpler proof and provide new estimates on the best constant involved. Using endpoint differentiation, we also obtain an improved version of a Moser-Trudinger-Onofri type inequality on the sphere. As an immediate consequence, we derive an improved version of the Onofri inequality on the Euclidean space using the stereographic projection.
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https://hal.archives-ouvertes.fr/hal-00972035
Contributor : Gaspard Jankowiak <>
Submitted on : Tuesday, July 15, 2014 - 5:42:33 PM
Last modification on : Friday, December 11, 2020 - 9:38:02 AM
Long-term archiving on: : Monday, November 24, 2014 - 1:41:31 PM

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  • HAL Id : hal-00972035, version 2
  • ARXIV : 1404.1028

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Gaspard Jankowiak, van Hoang Nguyen. Fractional Sobolev and Hardy-Littlewood-Sobolev inequalities. 2014. ⟨hal-00972035v2⟩

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