Note on Fourier inequalities
We prove that the Hausdorff-Young inequality parallel to(f) over cap parallel to(q(center dot)) <= C parallel to F parallel to(p(center dot)) with q(x) = p '(1/x) and p(center dot) even and non-decreasing holds in variable Lebesgue spaces if and only if p is a constant. However, under the ad...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/489170 |
| Acceso en línea: | http://hdl.handle.net/2072/489170 |
| Access Level: | acceso abierto |
| Palabra clave: | Fourier transform Variable Lebesgue space Weighted Fourier inequalities Hardy-Littlewood type theorem |
| Sumario: | We prove that the Hausdorff-Young inequality parallel to(f) over cap parallel to(q(center dot)) <= C parallel to F parallel to(p(center dot)) with q(x) = p '(1/x) and p(center dot) 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 complete characterization of Pitt-type weighted Fourier inequalities in both the classical and variable Lebesgue setting. |
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