Revista de la
Unión Matemática Argentina
Interpolation theory for the HK-Fourier transform
Juan H. Arredondo and Alfredo Reyes
Volume 62, no. 2 (2021), pp. 401–413    

https://doi.org/10.33044/revuma.1911

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Abstract

We use the Henstock–Kurzweil integral and interpolation theory to extend the Fourier cosine transform operator, broadening some classical properties such as the Riemann–Lebesgue lemma. Furthermore, we show that a qualitative difference between the cosine and sine transform is preserved on differentiable functions.