The Fourier transform in Lebesgue spaces
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915171772923904 |
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| author | Talvila, Erik |
| author_facet | Talvila, Erik |
| contents | 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 Fourier transforms is isometrically isomorphic to $L^p({\mathbb R)}$. There is an exchange theorem and inversion in norm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_01699 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Fourier transform in Lebesgue spaces Talvila, Erik Classical Analysis and ODEs Primary 42A38, 46F10 (Primary) 26A42, 46B04 (Secondary) 26A42, 46B04 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 Fourier transforms is isometrically isomorphic to $L^p({\mathbb R)}$. There is an exchange theorem and inversion in norm. |
| title | The Fourier transform in Lebesgue spaces |
| topic | Classical Analysis and ODEs Primary 42A38, 46F10 (Primary) 26A42, 46B04 (Secondary) 26A42, 46B04 |
| url | https://arxiv.org/abs/2309.01699 |