Singular integrals and rectifiability

We shall discuss singular integrals on lower dimensional subsets of $\mathbf{R}^n$. A survey of this topic was given in [M4]. The first part of this paper gives a quick review of some results discussed in [M4] and a survey on some newer results and open problems. In the second part we prove some results on the Riesz kernels in $\mathbf{R}^n$. As far I know, they have not been explicitly stated and proved, but they are very closely related to some earlier results and methods.