Convolution Operators on Discrete Hardy Spaces

We establish the connection between the boundedness of convolution operators on Hp(ℝN) and some related operators on Hp(ℤN). 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 type belonging to Hardy spaces