Multiple Weighted Norm Inequalities for Multilinear Strongly Singular Integral Operators with Generalized Kernels

Lin (Nonlinear Anal 192:111699, 2020) introduced a class of multilinear strongly singular integral operators, which have weaker smoothness condition compared to the classical multilinear singular integral operators except that they do not require the size condition. In this paper, the smoothness condition of the kernel function is further reduced of the multilinear strongly singular integral operator. We get the weighted L^p boundedness of the multilinear strongly singular integral operator with generalized kernel as well as two types of endpoint estimates, respectively. Additionally, the weighted L^p boundedness of the multilinear commutator and multilinear iterated commutator generated by BMO functions and multilinear strongly singular integral operators with generalized kernels is also established, respectively.