Multilinear commutators of multilinear strongly singular integral operators with generalized kernels

In [S. Yang and Y. Lin, Multilinear strongly singular integral operators with generalized kernels and applications, AIMS Math. 6 (2021), no. 12, 13533-13551], the authors of the present paper further weaken the smoothness condition of kernel functions with multilinear strongly singular Calderon-Zygmund operators of [Y. Lin, Multilinear theory of strongly singular Calderon-Zygmund operators and applications, Nonlinear Anal. 192 (2020), Article ID 111699]. They defined a new class of multilinear strongly singular integral operators, and studied its weighted L-p boundedness, variable exponent L-p(center dot) boundedness and endpoint estimates. In this paper, we naturally consider the boundedness of multilinear commutators and multilinear iterated commutators, which are generated by multilinear strongly singular integral operators with generalized kernels and Lipschitz functions. Our results include the corresponding results of multilinear strongly singular Calderon-Zygmund operators and classical multilinear Calderon-Zygmund operators, respectively.