Weak-type boundedness of the Fourier transform on rearrangement invariant function spaces

We study several questions about the weak-type boundedness of the Fourier transform ℱ on rearrangement invariant spaces. In particular, we characterize the action of ℱ as a bounded operator from the minimal Lorentz space Λ(X) into the Marcinkiewicz maximal space M(X), both associated with a rearrang...

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Detalles Bibliográficos
Autores: Boza, Santiago, Soria de Diego, F. Javier
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2018
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:2445/140062
Acceso en línea:https://hdl.handle.net/2445/140062
Access Level:acceso abierto
Palabra clave:Transformacions de Fourier
Espais de Lorentz
Fourier transformations
Lorentz spaces
Descripción
Sumario:We study several questions about the weak-type boundedness of the Fourier transform ℱ on rearrangement invariant spaces. In particular, we characterize the action of ℱ as a bounded operator from the minimal Lorentz space Λ(X) into the Marcinkiewicz maximal space M(X), both associated with a rearrangement invariant space X. Finally, we also prove some results establishing that the weak-type boundedness of ℱ, in certain weighted Lorentz spaces, is equivalent to the corresponding strong-type estimates.