The Fourier transform in Lebesgue spaces

期刊论文
发表日期：

2024年3月6日

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Erik Talvila

摘要

For each f ∈ L^p(ℝ) (1 ⩽ p < ∞) 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(ℝ). There is an exchange theorem and inversion in norm.