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Discrete analogues of maximally modulated singular integrals of Stein-Wainger type: ℓp bounds for p > 1.

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Title: Discrete analogues of maximally modulated singular integrals of Stein-Wainger type: ℓp bounds for p > 1.
Authors: Krause, Ben1 (AUTHOR) ben.krause@kcl.ac.uk, Roos, Joris1,2,3 (AUTHOR) joris_roos@uml.edu
Source: Journal of Functional Analysis. Nov2023, Vol. 285 Issue 10, pN.PAG-N.PAG. 1p.
Subjects: Hardy-Littlewood method, Singular integrals
Abstract: It is proved that certain discrete analogues of maximally modulated singular integrals of Stein-Wainger type are bounded on ℓ p (Z n) for all p ∈ (1 , ∞). This extends earlier work of the authors concerning the case p = 2. Some open problems for further investigation are briefly discussed. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:It is proved that certain discrete analogues of maximally modulated singular integrals of Stein-Wainger type are bounded on ℓ p (Z n) for all p ∈ (1 , ∞). This extends earlier work of the authors concerning the case p = 2. Some open problems for further investigation are briefly discussed. [ABSTRACT FROM AUTHOR]
ISSN:00221236
DOI:10.1016/j.jfa.2023.110123