Improved L${}^p$-Poincaré inequalities on the hyperbolic space

Elvise Berchio, Lorenzo D'Ambrosio, Debdip Ganguly +1

We investigate the possibility of improving the $p$-Poincaré inequality $\Vert {\nabla }_{{\mathbb{H}}^N}u{\Vert }_p\ge {\Lambda }_p\Vert u{\Vert }_p$ on the hyperbolic space, where $p>2$ and $Λ_p:=[(N-1)/p]^{p}…