The positive part of a Fourier transform

Journal of the Australian Mathematical Society

Augusto Logli¹ 

关键词: 42 B 10;   

DOI  :  10.1017/S1446788700022990

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

We consider the function u whose Fourier transform is the positive part of the Fourier transform of a function f on Rn. If n ≤ 2 and f satisfies simple regularity conditions (in particular if f is in the Schwartz space Y(Rn), then u lies in L1(Rn). If n ≥ 3, then simple counterexamples exist; for example, if f(x) = |x|2 exp(-|x|2), then u does not lie in L1(Rn).

【 授权许可】

Unknown