On the uniform rectifiability of AD regular measures with bounded Riesz transform operator: the case of codimension 1

Fedor Nazarov, Xavier Tolsa, Alexander Volberg

We prove that if $\mu$ is a d-dimensional Ahlfors-David regular measure in ${\mathbb{R}}^{d+1}$, then the boundedness of the $d$-dimensional Riesz transform in $L^2(\mu )$ implies that the non-BA…