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

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