Weak-Type Boundedness of the Fourier Transform on Rearrangement Invariant Function Spaces

Santiago Boza, Javier Soria
2018 Proceedings of the Edinburgh Mathematical Society  
AbstractWe 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
more » ... esponding strong-type estimates.
doi:10.1017/s0013091518000032 fatcat:sbxdjadv6rcgvf527egirccohe