Define the Riesz transform in singular integral form
\begin{equation*} R_jf(x)=\lim_{\epsilon\to 0}\pi^{\frac{-(n+1)}{2}}\Gamma(\frac{n+1}{2})\int_{|y|>\epsilon}\frac{y_jf(x-y)}{|y|^{n+1}}dy. \end{equation*}
I know it is a generalisation of the Hilbert transform. They are clearly of the same form, both p.v integrals, convolution operators, except the Riesz transforms is in a generalised vectorial form for the $j^{th}$ component. What about the constants in front of the integral? Any thoughts or comments are welcome.