On the maximum principle for the Riesz transform

Vladimir Eiderman, Fedor Nazarov

Let $\mu$ be a measure in ${\mathbb{R}}^d$ with compact support and continuous density, and let $$R^s\mu (x)=\int \frac{y-x}{|y-x{|}^{s+1}}d\mu (y),x,y\in {\mathbb{R}}^d,0<s<d.$$ We cons…