Optimal estimates for hyperbolic harmonic mappings in Hardy space

Jiaolong Chen, David Kalaj

Assume that $p\in (1,\infty ]$ and $u=P_h[\varphi ]$, where $\varphi \in L^p({\mathbb{S}}^{n-1},{\mathbb{R}}^n)$. Then for any $x\in {\mathbb{B}}^n$, we obtain the sharp inequalities $$ |u(x)|\l…