Convolution operators on discrete Hardy spaces

We establish the connection between the boundedness of convolution operators on H-P(R-N) and some related operators on H-p(Z(N)). The results we obtain here extend the already known for Lp spaces With p > 1. We also study similar results for maximal operators given by convolution with the dilation of a fixed kernel. Our main tools are some known results about functions of exponential type already presented in [BC1] that, in particular, allow us to prove a sampling theorem for functions of exponential ta pe belonging to Hardy spaces.