Optimal Rearrangement-Invariant Banach Function Range for the Hilbert Transform

Kanat Tulenov

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

Optimal Rearrangement-Invariant Banach Function Range for the Hilbert Transform

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Authors

Kanat Tulenov

DOI:

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

Keywords:

rearrangement-invariant Banach function space, Hilbert transform, optimal range

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.

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Published

2021-06-30

How to Cite

Tulenov, K. (2021). Optimal Rearrangement-Invariant Banach Function Range for the Hilbert Transform. Eurasian Mathematical Journal, 12(2), 90–103. https://doi.org/10.32523/2077-9879-2021-12-2-90-103