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 Eurasian Math. J., 2021, Volume 12, Number 2, Pages 90–103 (Mi emj407)

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

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.

DOI: https://doi.org/10.32523/2077-9879-2021-12-2-90-103

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MSC: 46E30, 44A15, 47L20, 47C15
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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
\Bibitem{Tul21} \by K.~S.~Tulenov \paper Optimal rearrangement-invariant Banach function range for the Hilbert transform \jour Eurasian Math. J. \yr 2021 \vol 12 \issue 2 \pages 90--103 \mathnet{http://mi.mathnet.ru/emj407} \crossref{https://doi.org/10.32523/2077-9879-2021-12-2-90-103} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85099218278}