Note on Fourier inequalities
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909245938597888 |
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| author | Saucedo, Miquel Tikhonov, Sergey |
| author_facet | Saucedo, Miquel Tikhonov, Sergey |
| contents | We prove that the Hausdorff--Young inequality $\|{\widehat{f}}\|_{q(\cdot)} \leq C \|{f}\|_{p(\cdot)}$ with $q(x)=p'(1/x)$ and $p(\cdot)$ even and non-decreasing holds in variable Lebesgue spaces if and only if $p$ is a constant. However, under the additional condition on monotonicity of $f$, we obtain a full characterization of Pitt-type weighted Fourier inequalities in the classical and variable Lebesgue setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05503 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Note on Fourier inequalities Saucedo, Miquel Tikhonov, Sergey Classical Analysis and ODEs 42B10 We prove that the Hausdorff--Young inequality $\|{\widehat{f}}\|_{q(\cdot)} \leq C \|{f}\|_{p(\cdot)}$ with $q(x)=p'(1/x)$ and $p(\cdot)$ even and non-decreasing holds in variable Lebesgue spaces if and only if $p$ is a constant. However, under the additional condition on monotonicity of $f$, we obtain a full characterization of Pitt-type weighted Fourier inequalities in the classical and variable Lebesgue setting. |
| title | Note on Fourier inequalities |
| topic | Classical Analysis and ODEs 42B10 |
| url | https://arxiv.org/abs/2407.05503 |