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

$\ell^p\big(\mathbb Z^d\big)$-estimates for discrete operators of Radon type: Maximal functions and vector-valued estimates