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

TL;DR

This paper establishes boundedness results for specific commutators of multilinear strongly singular integrals on non-homogeneous metric measure spaces, expanding the understanding of such operators in complex geometric contexts.

Contribution

It introduces new boundedness results for iterated and summation form commutators generated by multilinear strongly singular integrals on non-homogeneous spaces.

Findings

Boundedness of iterated commutators in Lebesgue spaces

Boundedness of summation form commutators in Lebesgue spaces

Extension of singular integral theory to non-homogeneous metric 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.