A Necessary Condition for HK-Integrability of the Fourier Sine Transform Function
| Authors | |
|---|---|
| Year of publication | 2023 |
| Type | Article in Periodical |
| Magazine / Source | Czechoslovak Mathematical Journal |
| MU Faculty or unit | |
| Citation | |
| Web | https://doi.org/10.21136/CMJ.2023.0257-22 |
| Doi | http://dx.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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