  Fix $d\geq 2$, and $s\in (d-1,d)$. We characterize the non-negative locally
finite non-atomic Borel measures $\mu$ in $\mathbb{R}^d$ for which the
associated $s$-Riesz transform is bounded in $L^2(\mu)$ in terms of the Wolff
energy. This extends the range of $s$ in which the Mateu-Prat-Verdera
characterization of measures with bounded $s$-Riesz transform is known.
  As an application, we give a metric characterization of the removable sets
for locally Lipschitz continuous solutions of the fractional Laplacian operator
$(-\Delta)^{\alpha/2}$, $\alpha\in (1,2)$, in terms of a well-known capacity
from non-linear potential theory. This result contrasts sharply with
removability results for Lipschitz harmonic functions.
