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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Detalles Bibliográficos
Autor: Oganesyan, K.
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
Descripción
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).