On multilinear oscillatory singular integrals with rough kernels

In this paper, for the multilinear oscillatory singular integral operators T-A defined by [GRAPHICS] where P(x, y) is a nontrivial and real-valued polynomial defined on R-n x R-n, Omega(x) is homogeneous of degree zero on R-n, A(x) has derivatives of order m in <(Lambda)over dot> (0 < beta < 1), Rm+1 (A; x, y) denotes the (m + 1)th remainder of the Taylor series of A at x expended about y, the author proves that if Omega is an element of L-q(Sn-1) for some q > 1/(1 - beta), then for any p is an element of (1, infinity), T-A is bounded on L-p(R-n). Meanwhile, the weighted L-p-boundedness of T-A is also given. (C) 2004 Elsevier I ic. All rights reserved.