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

Abstract

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.

Locations

• Proceedings of the Edinburgh Mathematical Society - View
• Dipòsit Digital de la Universitat de Barcelona (Universitat de Barcelona) - View - PDF
• UPCommons institutional repository (Universitat Politècnica de Catalunya) - View - PDF