The authors 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..
The authors 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