Abstract
In this paper we establish local versions of the Onofri and sharp Sobolev inequalities. Such local inequalities enable us to give a more direct and simpler proof of the Onofri inequality on 𝕊2, as well as an alternative proof of sharp Sobolev inequalities on 𝕊n (for n ≥ 3). © 2005 Wiley Periodicals, Inc.
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