A sharp Sobolev inequality on the Caffarelli-Kohn-Nirenberg hyperbolic space

Baptiste Devyver, Louis Dupaigne, Pierre-Damien Thizy

In the Euclidean space ${\mathbb{R}}^d$, the sharp classical Sobolev inequality is equivalent by conformal invariance to a Sobolev inequality on the hyperbolic space ${\mathbb{H}}^d$.…