Commutators of multilinear singular integral operators on non-homogeneous metric measure spaces

TL;DR

This paper investigates the boundedness of commutators generated by multilinear singular integral operators with RBMO functions on non-homogeneous metric measure spaces, extending classical results to more general settings.

Contribution

It establishes boundedness results for these commutators on non-homogeneous spaces using a sharp maximal operator approach, a novel extension of existing theory.

Findings

Boundedness of commutators on non-homogeneous spaces proven

Utilizes sharp maximal operator technique for analysis

Extends classical results to more general metric measure spaces

Abstract

Let $(X,d,\mu)$ be a metric measure space satisfying both the geometrically doubling and the upper doubling measure conditions, which is called non-homogeneous metric measure space. In this paper, via a sharp maximal operator, the boundedness of commutators generated by multilinear singular integral with $RBMO(\mu)$ function on non-homogeneous metric measure spaces in $m$-multiple Lebesgue spaces is obtained.