Properties of the Fourier sine transform related to integrability framework of the HK- integral

Ponente(s): Manuel Bernal Gonzalez

The integrability of the Fourier sine transform has been studied by E. Liflyand in the framework of the Lebesgue integral on a subspace of locally absolutely and of bounded variation. With the introduction of the Henstock-Kurzweil integral, it is proved that the hypothesis that f/x is Lebesgue integrable, where f is a bounded variation function, is an optimal condition to achieve the integrability of the Fourier sine transform.