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

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.

15 pages; changed title, final version to appear in JFA

References in corpus (4)

• Maximal operators and Hilbert transforms along variable non-flat homogeneous curves
• Square function estimates for discrete Radon transforms
• Sharp variation-norm estimates for oscillatory integrals related to Carleson's theorem
• Discrete analogues of maximally modulated singular integrals of Stein-Wainger type