A Necessary Condition for HK-Integrability of the Fourier Sine Transform Function

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Authors	ARREDONDO Juan H. H. BERNAL Manuel MORALES MACIAS Maria Guadalupe
Year of publication	2025
Type	Article in Periodical
Magazine / Source	Czechoslovak Mathematical Journal
MU Faculty or unit	Faculty of Science
Citation
web	https://doi.org/10.21136/CMJ.2023.0257-22
Doi	https://doi.org/10.21136/CMJ.2023.0257-22
Keywords	Fourier transform; Henstock-Kurzweil integral; bounded variation function
Description	The paper is concerned with integrability of the Fourier sine transform function when f ? BV0(R), where BV0(R) is the space of bounded variation functions vanishing at infinity. It is shown that for the Fourier sine transform function of f to be integrable in the Henstock-Kurzweil sense, it is necessary that f/x ? L1(R). We prove that this condition is optimal through the theoretical scope of the Henstock-Kurzweil integration theory.
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