  We prove $\ell^p\big(\mathbb Z^d\big)$ bounds, for $p\in(1, \infty)$, of
discrete maximal functions corresponding to averaging operators and truncated
singular integrals of Radon type, and their applications to pointwise ergodic
theory. Our new approach is based on a unified analysis of both types of
operators, and also yields an extension to the vector-valued form of these
results.
