Integrability of the Sine Fourier Transform for Non-Lebesgue Integrable Functions

Ponente(s): Manuel Bernal Gonzalez

Within mathematical analysis, the Fourier transform---originally introduced by Jean-Baptiste Joseph Fourier---remains a fundamental tool. While it is traditionally studied under the framework of Lebesgue integration, certain functions that are not Lebesgue integrable still admit a well-defined sine Fourier transform when considered through more general notions of integration. In this work, we examine the conditions under which such integrability holds, emphasizing the role of generalized integrals in extending the applicability of the sine Fourier transform beyond the classical setting. These results contribute to a broader understanding of Fourier analysis on spaces of functions outside the Lebesgue paradigm.