A derivation of the sharp Moser-Trudinger-Onofri inequalities from the fractional Sobolev inequalities

2018/04/09 by Jingang Xiong, Xiong, Jingang
Mathematics · #Nonlinear Partial Differential Equations #Analytic and geometric function theory #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1804.02807

Abstract

We derive the sharp Moser-Trudinger-Onofri inequalities on the standard n-sphere and CR (2n+1)- sphere as the limit of the sharp fractional Sobolev inequalities for all n≥ 1. On the 2-sphere and 4-sphere, this was established recently by S.-Y. Chang and F. Wang. Our proof uses an alternative and elementary argument.

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