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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Author: Oganesyan, K.
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
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spelling Two-Dimensional Hardy–Littlewood Theorem for Functions with General Monotone Fourier CoefficientsOganesyan, K.Fourier seriesGeneral monotone coefficientsHardy–Littlewood theoremWe 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).The work was supported by the Moebius Contest Foundation for Young Scientists and the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS” (Grant no. 19-8-2-28-1)Birkhauser2023info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion30 p.application/pdfhttp://hdl.handle.net/2072/537053RECERCAT (Dipòsit de la Recerca de Catalunya)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésJournal of Fourier Analysis and ApplicationsL'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:recercat.cat:2072/5370532026-05-29T05:05:01Z
dc.title.none.fl_str_mv Two-Dimensional Hardy–Littlewood Theorem for Functions with General Monotone Fourier Coefficients
title Two-Dimensional Hardy–Littlewood Theorem for Functions with General Monotone Fourier Coefficients
spellingShingle Two-Dimensional Hardy–Littlewood Theorem for Functions with General Monotone Fourier Coefficients
Oganesyan, K.
Fourier series
General monotone coefficients
Hardy–Littlewood theorem
title_short Two-Dimensional Hardy–Littlewood Theorem for Functions with General Monotone Fourier Coefficients
title_full Two-Dimensional Hardy–Littlewood Theorem for Functions with General Monotone Fourier Coefficients
title_fullStr Two-Dimensional Hardy–Littlewood Theorem for Functions with General Monotone Fourier Coefficients
title_full_unstemmed Two-Dimensional Hardy–Littlewood Theorem for Functions with General Monotone Fourier Coefficients
title_sort Two-Dimensional Hardy–Littlewood Theorem for Functions with General Monotone Fourier Coefficients
dc.creator.none.fl_str_mv Oganesyan, K.
author Oganesyan, K.
author_facet Oganesyan, K.
author_role author
dc.subject.none.fl_str_mv Fourier series
General monotone coefficients
Hardy–Littlewood theorem
topic Fourier series
General monotone coefficients
Hardy–Littlewood theorem
description 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).
publishDate 2023
dc.date.none.fl_str_mv 2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/2072/537053
url http://hdl.handle.net/2072/537053
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Journal of Fourier Analysis and Applications
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 30 p.
application/pdf
dc.publisher.none.fl_str_mv Birkhauser
publisher.none.fl_str_mv Birkhauser
dc.source.none.fl_str_mv RECERCAT (Dipòsit de la Recerca de Catalunya)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,811543

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