Characterization of compactness of the commutators of bilinear fractional integral operators

TL;DR

This paper characterizes the compactness of commutators of bilinear fractional integral operators on Lebesgue spaces using mean oscillation properties, including weighted cases, advancing understanding of their boundedness and compactness.

Contribution

It provides a new characterization of compactness for these commutators based on mean oscillation, extending to weighted Lebesgue spaces.

Findings

Characterization of compactness via mean oscillation properties.

Extension of results to weighted Lebesgue spaces.

New criteria for compactness of bilinear fractional integral commutators.

Abstract

The compactness of the commutators of bilinear fractional integral operators and point-wise multiplication, acting on products of Lebesgue spaces, is characterized in terms of appropriate mean oscillation properties of their symbols. The compactness of the commutators when acting on product of weighted Lebesgue spaces is also studied.