Multilinear fractional integral operators on non-homogeneous metric measure spaces

TL;DR

This paper establishes the boundedness of multilinear fractional integral operators and their commutators on non-homogeneous metric measure spaces, extending classical harmonic analysis results to more general settings.

Contribution

It proves boundedness results for multilinear fractional integrals and their commutators on non-homogeneous spaces with new techniques involving sharp maximal operators.

Findings

Boundedness of multilinear fractional integral operators on non-homogeneous spaces.

Boundedness of commutators with RBMO functions in Lebesgue spaces.

Extension of harmonic analysis tools to non-homogeneous metric measure spaces.

Abstract

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