Analysis & PDE
- Anal. PDE
- Volume 12, Number 5 (2019), 1259-1272.
Sparse bounds for the discrete cubic Hilbert transform
Consider the discrete cubic Hilbert transform defined on finitely supported functions on by
We prove that there exists and universal constant such that for all finitely supported on there exists an -sparse form for which
This is the first result of this type concerning discrete harmonic analytic operators. It immediately implies some weighted inequalities, which are also new in this setting.
Anal. PDE, Volume 12, Number 5 (2019), 1259-1272.
Received: 9 November 2017
Accepted: 5 July 2018
First available in Project Euclid: 5 January 2019
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Culiuc, Amalia; Kesler, Robert; Lacey, Michael T. Sparse bounds for the discrete cubic Hilbert transform. Anal. PDE 12 (2019), no. 5, 1259--1272. doi:10.2140/apde.2019.12.1259. https://projecteuclid.org/euclid.apde/1546657232