Czechoslovak Mathematical Journal, first online, pp. 1-13
The Fourier transform in Lebesgue spaces
Erik Talvila
Received January 1, 2023. Published online March 6, 2024.
Abstract: For each $f\in L^p({\mathbb R)}$ ($1\leq p<\infty$) it is shown that the Fourier transform is the distributional derivative of a Hölder continuous function. For each $p$, a norm is defined so that the space of Fourier transforms is isometrically isomorphic to $L^p({\mathbb R)}$. There is an exchange theorem and inversion in norm.
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Affiliations: Erik Talvila Department of Mathematics & Statistics, University of the Fraser Valley, 33844 King Road, Abbotsford, BC Canada V2S 7M8, e-mail: Erik.Talvila@ufv.ca
