AN EXTENSION OF SOME PROPERTIES FOR THE FOURIER TRANSFORM OPERATOR ON L-P(R) SPACES

作者：Guadalupe Morales M; Arredondo Juan H^*; Mendoza Francisco J

来源：Union Matematica Argentina. Revista, 2016, 57(2): 85-94.

• Fourier transform
• L-p(R) space
• Henstock-Kurzweil integral

In this paper the Fourier transform is studied using the Henstock-Kurzweil integral on R. We obtain that the classical Fourier transform F-p : L-P (R) -> L-q (R), 1/p + 1/q = 1 and 1 < p <= 2, is represented by the integral on a subspace of L-P (R), which strictly contains L-1 (R) boolean AND L-P (R). Moreover, for any function f in that subspace, F-p (f) obeys a generalized Riemann Lebesgue lemma.

• 出版日期2016