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2019 Sparse bounds for the discrete cubic Hilbert transform
Amalia Culiuc, Robert Kesler, Michael T. Lacey
Anal. PDE 12(5): 1259-1272 (2019). DOI: 10.2140/apde.2019.12.1259

Abstract

Consider the discrete cubic Hilbert transform defined on finitely supported functions f on by

H 3 f ( n ) = m 0 f ( n m 3 ) m .

We prove that there exists r<2 and universal constant C such that for all finitely supported f,g on there exists an (r,r)-sparse form Λr,r for which

| H 3 f , g | C Λ r , r ( f , g ) .

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.

Citation

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Amalia Culiuc. Robert Kesler. Michael T. Lacey. "Sparse bounds for the discrete cubic Hilbert transform." Anal. PDE 12 (5) 1259 - 1272, 2019. https://doi.org/10.2140/apde.2019.12.1259

Information

Received: 9 November 2017; Accepted: 5 July 2018; Published: 2019
First available in Project Euclid: 5 January 2019

zbMATH: 07006761
MathSciNet: MR3892403
Digital Object Identifier: 10.2140/apde.2019.12.1259

Subjects:
Primary: 11L03, 42A05

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.12 • No. 5 • 2019
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