Radial limits of inner functions and Bloch spaces

Let $f$ be an inner function in the unit ball $B_n \subset\mathbb{C}^n$, $n\ge 1$. Assume that

$$\sup_{z\in B_n} \frac{\vert\mathcal{R} f(z)\vert(1-\vert z\vert^2)^{1+\beta}}{\left(1-\vert f(z)\vert^2 \right)^2} < \infty,$$

where $\beta\in (0,1)$ and $\mathcal{R} f$ is the radial derivative. Then, for all $\alpha\in\partial B_1$, the set $\{\zeta\in \partial B_n:\, f^*(\zeta) =\alpha\}$ has a non-zero real Hausdorff $t^{2n-1-\beta}$-content, and it has a non-zero complex Hausdorff $t^{n-\beta}$-content.