Commutators of multilinear strongly singular integrals on non-homogeneous metric measure spaces

Abstract

Let $(X,d,\mu)$ denotes non-homogeneous metric measure space satisfying geometrically doubling and the upper doubling measure condition. In this paper, the boundedness in Lebesgue spaces for two kinds of commutators, which are iterated commutators and commutators in summation form, generated by multilinear strongly singular integral operators with RBMO$(\mu)$ function on non-homogeneous metric measure spaces $(X,d,\mu)$ is obtained.