  We show $\ell^p\big(\mathbb Z^d\big)$ boundedness, for $p\in(1, \infty)$, of
discrete singular integrals of Radon type with the aid of appropriate square
function estimates, which can be thought as a discrete counterpart of the
Littlewood--Paley theory. It is a very powerful approach which allows us to
proceed as in the continuous case.
