Optimal Rearrangement-Invariant Banach Function Range for the Hilbert Transform - Tulenov, Kanat (Eurasian Mathematical Journal, 2021)
We describe the optimal rearrangement-invariant Banach function range of the classical Hilbert transform acting on a rearrangement-invariant Banach function space. We also show the existence of such optimal range for the Lorentz and Marcinkiewicz spaces.