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arXiv · 2506.08891

The Fourier transform in variable exponent Lebesgue spaces

André Pedroso Kowacs·Wagner Augusto Almeida de Moraes
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Abstract

In this work we define a Fourier transform for each $f\in L^{p(\cdot)}(\mathbb{R})$, for a large class of exponent functions $p(\cdot)$, as the distributional derivative of a H\"older continuous function. A norm is defined in the space of such Fourier transforms so that it is isometrically isomorphic to $L^{p(\cdot)}(\mathbb{R})$. We also prove several properties of this Fourier transform, such as inversion in norm and an exchange theorem.

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André Pedroso Kowacs, Wagner Augusto Almeida de Moraes. 2025-06-10. The Fourier transform in variable exponent Lebesgue spaces. https://arxiv.org/abs/2506.08891

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