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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| Formato: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:283439 |
| Acesso em linha: | https://ddd.uab.cat/record/283439 https://dx.doi.org/urn:doi:10.1007/s00041-023-10039-x |
| Access Level: | acceso abierto |
| Palavra-chave: | Fourier series General monotone coefficients Hardy-Littlewood theorem |
| Resumo: | 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. |
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