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Weak-Type Boundedness of the Fourier Transform on Rearrangement Invariant Function Spaces
Published online by Cambridge University Press: 08 June 2018
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.
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 61 , Issue 3 , August 2018 , pp. 879 - 890
- Copyright
- Copyright © Edinburgh Mathematical Society 2018
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