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.

Lin (Nonlinear Anal 192:111699, 2020)引入了一类多线性强奇异积分算子，与经典多线性奇异积分算子相比，除了不需要大小条件外，其平滑性条件较弱。本文进一步降低了多线性强奇异积分算子的核函数光滑条件。我们分别得到了具有广义核的多线性强奇异积分算子的加权\(L^p\)有界性以及两种类型的端点估计。另外，BMO生成的多线性换向器和多线性迭代换向器的加权\(L^p\)有界性还分别建立了函数和具有广义核的多线性强奇异积分算子。