Discrete analogues of maximally modulated singular integrals of Stein-Wainger type

Ben Krause; Joris Roos

doi:10.4171/JEMS/1160

Discrete analogues of maximally modulated singular integrals of Stein-Wainger type

Ben Krause, Joris Roos

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Consider the maximal operator C f .x/ D sup 2R X y2Znn10 f .x - y/e. jyj2d /K.y/.x 2 Zn/; where d is a positive integer, K a Calderon-Zygmund kernel and n ≥ 1. This is a discrete analogue of a real-variable operator studied by Stein and Wainger. The nonlinearity of the phase introduces a variety of new difficulties that are not present in the real-variable setting. We prove 2.Zn/-bounds for C , answering a question posed by Lillian Pierce.

Original language	English
Pages (from-to)	3183-3213
Number of pages	31
Journal	Journal of the European Mathematical Society
Volume	24
Issue number	9
DOIs	https://doi.org/10.4171/JEMS/1160
Publication status	Published - 2022

Keywords

circle method
Discrete analogues
Stein-Wainger type operators

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author = "Ben Krause and Joris Roos",

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AU - Roos, Joris

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AB - Consider the maximal operator C f .x/ D sup 2R X y2Znn10 f .x - y/e. jyj2d /K.y/.x 2 Zn/; where d is a positive integer, K a Calderon-Zygmund kernel and n ≥ 1. This is a discrete analogue of a real-variable operator studied by Stein and Wainger. The nonlinearity of the phase introduces a variety of new difficulties that are not present in the real-variable setting. We prove 2.Zn/-bounds for C , answering a question posed by Lillian Pierce.

KW - circle method

KW - Discrete analogues

KW - Stein-Wainger type operators

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JF - Journal of the European Mathematical Society

IS - 9

ER -

Discrete analogues of maximally modulated singular integrals of Stein-Wainger type

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Keywords

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