Non-existence of reflectionless measures for the s-Riesz transform when 0<s<1

Laura Prat, Xavier Tolsa

A measure $\mu$ on ${\mathbb{R}}^d$ is called reflectionless for the $s$-Riesz transform if the singular integral $R^s\mu (x)=\int \frac{y-x}{|y-x{|}^{s+1}}d\mu (y)$ is constant on the suppo…