Discrete nature of multivariate Paley-Wiener space  

作　　者：CHEN Guanggui and FANG Gensun(Department of Mathematlcs, Beijing Normal University, Beijing 100875, China) 

出　　处：《Progress in Natural Science:Materials International》2003年第4期300-303,共4页自然科学进展·国际材料（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No. 10071006) and Research Fund for the Doctoral Program Higher Education

摘　　要：Eoff proves that the univariate Paiey-Wiener space Bπ,p(R) is isomorphic to the discrete Hardy space Hp(Z), 0<p≤1, and our previous work shows that there are analogous results for multivariate Paley-Wiener space Bπ.p(R), if p = 1. In this paper,we continue our research and prove that the multivariate Paley-Wiener space Bπ.p(Rn) is isomorphic to the discrete Hardy space Hp(Zn), 0<p< 1, which closes the gap of our and Eoff s results.Eoff proves that the univariate Paley-Wiener space Bπ,p(R) is isomorphic to the discrete Hardy space Hp(R), 0<p≤1, and our previous work shows that there are analogous results for multivariate Paley-Wiener space Bπ,p(Rn), if p=1. In this paper, we continue our research and prove that the multivariate Paley-Wiener space Bπ,p(Rn) is isomorphic to the discrete Hardy space Hp(Rn), 0<p<1, which closes the gap of our and Eoff's results.

关 键 词：multivariate Paley-Wiener space discrete Hilbert transform discrete Hardy space. 

分 类 号：O158[理学—数学]