Weak-type boundedness of the Fourier transform on rearrangement invariant function spacest
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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 ¿(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.
CitationBoza, S., Soria, J. Weak-type boundedness of the Fourier transform on rearrangement invariant function spacest. "Proceedings of the Edinburgh Mathematical Society", 8 Juny 2018, vol. 61, núm. 3, p. 879-890.