Tulenov, K. S. Optimal rearrangement-invariant Banach function range for the Hilbert transform. (English) Zbl 1488.46065 Eurasian Math. J. 12, No. 2, 90-103 (2021). Summary: 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. Cited in 1 Document MSC: 46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 44A15 Special integral transforms (Legendre, Hilbert, etc.) Keywords:rearrangement-invariant Banach function space; Hilbert transform; optimal range PDFBibTeX XMLCite \textit{K. S. Tulenov}, Eurasian Math. J. 12, No. 2, 90--103 (2021; Zbl 1488.46065) Full Text: MNR