  Assume that $\Delta_h$ is the hyperbolic Laplacian in the unit ball
$\mathbb{B}$ and assume that $\Phi_n$ is the unique radial solution of Poisson
equation $\Delta_h \log \Phi_n =-4 (n-1)^2$ satisfying the condition
$\Phi_n(0)=1$ and $\Phi_n(\zeta)=0$ for $\zeta\in \partial\mathbb{B}$. We
explicitly solve the question of maximizing $$ R_n(f,\Omega)= \frac{\int_\Omega
|f(x)|^2 \Phi_n^\alpha(|x|) \, d\tau(x)}{\|f\|^2_{\mathbf{B}^2_\alpha}}, $$
over all $f \in\mathbf{B}^2_\alpha$ and $\Omega \subset \mathbb{B}$ with
$\tau(\Omega) = s,$ where $d\tau$ denotes the invariant measure on
$\mathbb{B},$ and $\|f\|_{{B}^2_\alpha}^2 = \int_\mathbb{B} |f(x)|^2
\Phi_n^\alpha(|x|) d\tau(x) < \infty.$
  This result extends the main result of Tilli and the second author
\cite{ramostilli} to a higher-dimensional context. Our proof relies on a
version of the techniques used for the two-dimensional case, with several
additional technical difficulties arising from the definition of the weights
$\Phi_n$ through hypergeometric functions. Additionally, we show that an
immediate relationship between a concentration result for log-sunharmonic
functions and one for the Wavelet transform is only available in dimension one.
