About an existence theorem of the Henstock-Fourier transform

Mendoza Torres, Francisco Javier ^[1] ; Escamilla Reyna, Juan Alberto ^[1] ; Raggi Cárdenas, María Guadalupe ^[1]
1. [1] Benemérita Universidad Autónoma de Puebla
  
  Benemérita Universidad Autónoma de Puebla
  
  México
Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 27, Nº. 3, 2008, págs. 307-318
Idioma: inglés
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Resumen
- 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.