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Eurasian Mathematical Journal, 2021, Volume 12, Number 2, Pages 90–103
DOI: https://doi.org/10.32523/2077-9879-2021-12-2-90-103 (Mi emj407) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Optimal rearrangement-invariant Banach function range for the Hilbert transform

K. S. Tulenovab

a Department of Mechanics and Mathematics, Al-Farabi Kazakh National University, 71 Al-Farabi Ave., 050040 Almaty, Kazakhstan
b Institute of Mathematics and Mathematical Modeling, 125 Pushkin St, 050010 Almaty, Kazakhstan
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DOI: https://doi.org/10.32523/2077-9879-2021-12-2-90-103
Abstract: 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.
Keywords and phrases: rearrangement-invariant Banach function space, Hilbert transform, optimal range.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan AP08052004
This work was supported by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan, project no. AP08052004.
Received: 17.04.2020
Bibliographic databases:
Document Type: Article
MSC: 46E30, 44A15, 47L20, 47C15
Language: English
Citation: K. S. Tulenov, “Optimal rearrangement-invariant Banach function range for the Hilbert transform”, Eurasian Math. J., 12:2 (2021), 90–103
Citation in format AMSBIB
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\by K.~S.~Tulenov
\paper Optimal rearrangement-invariant Banach function range for the Hilbert transform
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\vol 12
\issue 2
\pages 90--103
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