Sharp constant for Poincaré-type inequalities in the hyperbolic space

Quôc-Anh Ngô, Van Hoang Nguyen

In this note, we establish a Poincaré-type inequality on the hyperbolic space ${\mathbb{H}}^n$, namely \[ \|u\|_{p} \leqslant C(n,m,p) \|\nabla^m_g u\|_{p} \] for any $u \in W^{m,p}(\…