This article is cited in 1 paper

Optimal rearrangement-invariant Banach function range for the Hilbert transform

K. S. Tulenov<sup>ab

a</sup> 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.

MSC: 46E30, 44A15, 47L20, 47C15

Received: 17.04.2020

Language: English

DOI: 10.32523/2077-9879-2021-12-2-90-103

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