This paper is devoted to the study on the $L^p$-mapping properties for a class of multilinear oscillatory singular integrals with polynomial phase and rough kernel. By means of the method of block decomposition for the kernel function, the authors show that for any non-trivial polynomial phase, the $L^p(\rz)$ boundedness of the multilinear oscillatory singular integral operators and that of the corresponding local multilinear singular integral operators are equivalent; and for any real-valued polynomial phase, the $L^p(\rz)$ boundedness of the multilinear oscillatory integral operators can be deduced from that of the corresponding multilinear singular integral operators.
"A class of multilinear oscillatory singular integrals related to block spaces." Tohoku Math. J. (2) 56 (3) 299 - 315, 2004. https://doi.org/10.2748/tmj/1113246668