Discrete nature of multivariate Paley-Wiener space

摘要

Eoff proves that the univariate Paley-Wiener space B_(π,p) (R) is isomorphic to the discrete Hardy space H~p (Z), 0< p ≤ 1, and our previous work shows that there are analogous results for multivariate Paley-Wiener space B_(π,p) (R~n), if p = 1. In this paper, we continue our research and prove that the multivariate Paley-Wiener space B _(π,p) (R~n ) is isomorphic to the discrete Hardy space H~p(Z~n ), 0 < p < 1, which closes the gap of our and Eoff's results.