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Title: Weak-type boundedness of the Fourier transform on rearrangement invariant function spaces
Author: Boza, Santiago
Soria de Diego, F. Javier
Keywords: Transformacions de Fourier
Espais de Lorentz
Fourier transformations
Lorentz spaces
Issue Date: 8-Jun-2018
Publisher: Cambridge University Press
Abstract: 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.
Note: Versió postprint del document publicat a:
It is part of: Proceedings of the Edinburgh Mathematical Society, 2018, vol. 61, num. 3, p. 879-890
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ISSN: 0013-0915
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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