In this paper, by using the atomic decomposition of the weighted weak Hardy space WH_ω~1(R^n), the authors discuss a class of multilinear oscillatory singular integrals and obtain their boundedness from the weighted weak Hardy space WH_ω~1(R^n) to the weighted weak Lebesgue space WL_ω~1(R^n) for ω∈A_1(R^n).
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