The Fourier transform in variable exponent Lebesgue spaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912422712836096 |
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| author | Kowacs, André Pedroso de Moraes, Wagner Augusto Almeida |
| author_facet | Kowacs, André Pedroso de Moraes, Wagner Augusto Almeida |
| contents | 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 Hölder 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08891 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Fourier transform in variable exponent Lebesgue spaces Kowacs, André Pedroso de Moraes, Wagner Augusto Almeida Classical Analysis and ODEs Primary: 42A38, 46E30. Secondary: 26A42, 46B04 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 Hölder 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. |
| title | The Fourier transform in variable exponent Lebesgue spaces |
| topic | Classical Analysis and ODEs Primary: 42A38, 46E30. Secondary: 26A42, 46B04 |
| url | https://arxiv.org/abs/2506.08891 |