Geodesic
Optimal rearrangement-invariant Banach function range for the Hilbert transform
Eurasian mathematical journal, Tome 12 (2021) no. 2, pp. 90-103

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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. 
@article{EMJ_2021_12_2_a9,
     author = {K. S. Tulenov},
     title = {Optimal rearrangement-invariant {Banach} function range for the {Hilbert} transform},
     journal = {Eurasian mathematical journal},
     pages = {90--103},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2021_12_2_a9/}
}
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K. S. Tulenov. Optimal rearrangement-invariant Banach function range for the Hilbert transform. Eurasian mathematical journal, Tome 12 (2021) no. 2, pp. 90-103. http://geodesic.mathdoc.fr/item/EMJ_2021_12_2_a9/