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arXiv · 2309.01699

The Fourier transform in Lebesgue spaces

Erik Talvila
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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 H\"older continuous function. For each $p$ a norm is defined so that the space Fourier transforms is isometrically isomorphic to $L^p({\mathbb R)}$. There is an exchange theorem and inversion in norm.

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Erik Talvila. 2023-09-04. The Fourier transform in Lebesgue spaces. https://arxiv.org/abs/2309.01699

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