\((L^p,L^q)\) estimates for multilinear oscillatory singular integrals with smooth phases. (Q1421065)

In this paper, the authors establish the weighted \((L^p, L^q)\) estimates for a class of multilinear oscillatory singular integrals with smooth phase, where \(1<p, q<\infty\). Certain endpoint estimates for \(p=\infty\) are also given. The multilinear singular integrals are a generalization of the classical Calderón-Zygmund singular integrals.