An extension of some properties for the Fourier transform operator on L p ( R ) spaces
2016; Unión Matemática Argentina; Volume: 57; Issue: 2 Linguagem: Inglês
ISSN
1669-9637
AutoresM. Guadalupe Morales, Juan H. Arredondo, Francisco J. Mendoza-Torres,
Tópico(s)Differential Equations and Boundary Problems
ResumoIn this paper the Fourier transform is studied using the Henstock–Kurzweil integral on R. We obtain that the classical Fourier transform Fp:Lp(R)→Lq(R), 1/p+1/q=1 and 1<p≤2, is represented by the integral on a subspace of Lp(R), which strictly contains L1(R)∩Lp(R). Moreover, for any function f in that subspace, Fp(f) obeys a generalized Riemann–Lebesgue lemma.
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