多元Paley-Wiener空间的离散性(英文)

The Discrete Nature of Multivariate Paley-Wiener Space

Eoff证明了单元Paley Wiener空间Bπ,p(R)与离散的Hardy空间HP(Z),0<p≤1是同构的,当p=1时对于多元Pa ley -Wiener空间,前期工作得出了类似的结果。本文作者在前期工作的基础上,证明了多元Paley Wiener空间Bπ,p(Rn)与离散的Hardy空间HP(Zn),0<p<1是同构的,因而填补了我们前期工作与Eoff的结果之间的空白。

Eoff proves that the univariate Paley-Wiendr space B_(π,p) (R) is isomorphic to the discrete Hardy space H^P (Z) ,0<p≤1 ,our previous work shows that there are analogous results for multivariate Paley-Wiener space B_(π,p) (R^n) ,is 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.