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2018-06-08

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/140062

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

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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.

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https://doi.org/10.1017/S0013091518000032

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Transformacions de Fourier, Espais de Lorentz

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Fourier transformations, Lorentz spaces

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BOZA, Santiago and SORIA DE DIEGO, F. Javier. Weak-type boundedness of the Fourier transform on rearrangement invariant function spaces. Proceedings of the Edinburgh Mathematical Society. 2018. Vol. 61, num. 3, pags. 879-890. ISSN 0013-0915. [consulted: 8 of October of 2026]. Available at: https://hdl.handle.net/2445/140062

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