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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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Proceedings of the Edinburgh Mathematical Society, 2018, vol. 61, num. 3, p. 879-890

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(c) Edinburgh Mathematical Society, 2018

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Articles publicats en revistes (Matemàtiques i Informàtica)

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