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arXiv · 1404.1028

Fractional Sobolev and Hardy-Littlewood-Sobolev inequalities

Gaspard Jankowiak·Van Hoang Nguyen
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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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BibTeXRIS

Gaspard Jankowiak, Van Hoang Nguyen. 2014-07-15. Fractional Sobolev and Hardy-Littlewood-Sobolev inequalities. https://arxiv.org/abs/1404.1028

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