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Fractional Sobolev and Hardy-Littlewood-Sobolev inequalities


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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Dates and versions

hal-00972035 , version 1 (03-04-2014)
hal-00972035 , version 2 (15-07-2014)



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