Two-Dimensional Hardy–Littlewood Theorem for Functions with General Monotone Fourier Coefficients
We prove the Hardy–Littlewood theorem in two dimensions for functions whose Fourier coefficients obey general monotonicity conditions and, importantly, are not necessarily positive. The sharpness of the result is given by a counterexample, which shows that if one slightly extends the considered clas...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| 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:2072/537053 |
| Acceso en línea: | http://hdl.handle.net/2072/537053 |
| Access Level: | acceso abierto |
| Palabra clave: | Fourier series General monotone coefficients Hardy–Littlewood theorem |
| Sumario: | We prove the Hardy–Littlewood theorem in two dimensions for functions whose Fourier coefficients obey general monotonicity conditions and, importantly, are not necessarily positive. The sharpness of the result is given by a counterexample, which shows that if one slightly extends the considered class of coefficients, the Hardy–Littlewood relation fails. © 2023, The Author(s). |
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