Resumo

MENDOZA TORRES, FRANCISCO JAVIER; ESCAMILLA REYNA, JUAN ALBERTO  e  RAGGI CARDENAS, MA. GUADALUPE. ABOUT AN EXISTENCE THEOREM OF THE HENSTOCK - FOURIER TRANSFORM. Proyecciones (Antofagasta) [online]. 2008, vol.27, n.3, pp. 307-318. ISSN 0716-0917.  doi: 10.4067/S0716-09172008000300006.

We show that if f is lying on the intersection of the space of Henstock-Kurzweil integrable functions and the space of the bounded variation functions in the neighborhood of ±8, then its Fourier Transform exists in all R. This result is more general than the classical result which enunciates that if f is Lebesgue integrable, then the Fourier Transform of f exists in all R, because we also have proved that there are functions which belong to the intersection of the space of the Henstock-Kurzweil integrable functions and the space of the bounded variation functions which are not Lebesgue integrable.

Palavras-chave : Henstock-Kurzweil Integral; Bounded Variation Function; Lebesgue Integral.