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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| Format: | article |
| Status: | Published version |
| Publication Date: | 2023 |
| Country: | España |
| Institution: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repository: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/537053 |
| Online Access: | http://hdl.handle.net/2072/537053 |
| Access Level: | Open access |
| Keyword: | Fourier series General monotone coefficients Hardy–Littlewood theorem |
| Summary: | 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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