Boundedness of Multilinear Oscillatory Singular Integral on Weighted Weak Hardy Spaces

Abstract

In this paper, by using the atomic decomposition of the weighted weak Hardy space $WH_\omega^1(\mathbb{R}^n)$, the authors discuss a class of multilinear oscillatory singular integrals and obtain their boundedness from the weighted weak Hardy space $WH_\omega^1(\mathbb{R}^n)$ to the weighted weak Lebesgue space $WL_\omega^1(\mathbb{R}^n)$ for $\omega\in A_1(\mathbb{R}^n)$.