Sharp Sobolev inequalities under first moment constraints

Rupert L. Frank, Tianling Jin, Hua-Yang Wang +1

Let $n\ge 2$ and $1<p<n$. We study sharp Sobolev inequalities on the round sphere ${\mathbb{S}}^n$ for functions $u\in W^{1,p}({\mathbb{S}}^n)$ satisfying $\int_{\mathbb{S}^n}x|u|^{np/…