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arXiv · 2107.14616

Discrete analogues of maximally modulated singular integrals of Stein-Wainger type: $\ell^p$ bounds for $p>1$

Ben Krause·Joris Roos
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Abstract

It is proved that certain discrete analogues of maximally modulated singular integrals of Stein-Wainger type are bounded on $\ell^p(\mathbb{Z}^n)$ for all $p\in (1,\infty)$. This extends earlier work of the authors concerning the case $p=2$. Some open problems for further investigation are briefly discussed.

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Ben Krause, Joris Roos. 2021-07-30. Discrete analogues of maximally modulated singular integrals of Stein-Wainger type: $\ell^p$ bounds for $p>1$. https://doi.org/10.1016/j.jfa.2023.110123

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