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...
| Autores: | , , , |
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| 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 |
| 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) |
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