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

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 $n\ge 1$. 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.

arXiv comment8 pages, incorporated invaluable suggestions from a referee

References in corpus (1)

• On energy functionals, Kahler-Einstein metrics, and the Moser-Trudinger-Onofri neighborhood

Cited by in corpus (1)

• Higher order Sobolev trace inequalities on balls revisited