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Fractional Sobolev and Hardy-Littlewood-Sobolev inequalities

Nguyen, Van Hoang; Jankowiak, Gaspard (2014), Fractional Sobolev and Hardy-Littlewood-Sobolev inequalities. https://basepub.dauphine.fr/handle/123456789/13102

Type
Document de travail / Working paper
External document link
http://hal.archives-ouvertes.fr/hal-00972035
Date
2014
Publisher
Université Paris-Dauphine
Published in
Paris
Pages
25
Metadata
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Author(s)
Nguyen, Van Hoang
Jankowiak, Gaspard cc
Abstract (EN)
This work focuses on an improved fractional Sobolev inequality with a remainder term involving the \HLS{} 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.
Subjects / Keywords
pseudodifferential operators; nonlinear diffusion; stereographic projection; best constant; Hardy-Littlewood-Sobolev inequality; Fractional Sobolev inequality