A Lorentz invariant sharp Sobolev inequality on the circle

Pengyu Le

We prove the following sharp Sobolev inequality on the circle $${\int }_{{\mathbb{S}}^1}[4(v^{\prime }{)}^2-v^2]\mathrm{d}\theta \ge -\frac{4{\pi }^2}{{\int }_{{\mathbb{S}}^1}{v}^{-2}\mathrm{d}\theta },$$ with…