Hardy–Littlewood-type theorems for Fourier transforms in Rd

We obtain Fourier inequalities in the weighted Lp spaces for any 1<p<∞ involving the Hardy–Cesàro and Hardy–Bellman operators. We extend these results to product Hardy spaces for p⩽1. Moreover, boundedness of the Hardy-Cesàro and Hardy-Bellman operators in various spaces (Lebesgue, Har...

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Detalhes bibliográficos
Autores: Dyachenko, M., Nursultanov, E., Tikhonov, S., Weisz, F.
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2022
País:España
Recursos:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositório:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2072/532582
Acesso em linha:http://hdl.handle.net/2072/532582
Access Level:Acceso aberto
Palavra-chave:Fourier transform
Hardy-Cesàro and Hardy-Bellman operators
Hardy–Littlewood theorem
Product Hardy spaces
Descrição
Resumo:We obtain Fourier inequalities in the weighted Lp spaces for any 1<p<∞ involving the Hardy–Cesàro and Hardy–Bellman operators. We extend these results to product Hardy spaces for p⩽1. Moreover, boundedness of the Hardy-Cesàro and Hardy-Bellman operators in various spaces (Lebesgue, Hardy, BMO) is discussed. One of our main tools is an appropriate version of the Hardy–Littlewood–Paley inequality ‖fˆ‖Lp′,q≲‖f‖Lp,q. © 2022 The Author(s)