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

Abstract

It is proved that certain discrete analogues of maximally modulated singular integrals of Stein-Wainger type are bounded on ℓp(Zn) 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.