Compactness properties of commutators of bilinear fractional integrals

TL;DR

This paper investigates the compactness properties of commutators involving bilinear fractional integrals and functions in BMO subspaces, revealing conditions under which these operators are jointly or separately compact.

Contribution

It establishes new compactness results for commutators of bilinear fractional integrals and related operators, extending understanding of their functional analytic properties.

Findings

Commutators with functions in a BMO subspace are jointly compact.

Fractional integral versions of the bilinear Hilbert transform are separately compact.

The results generalize previous compactness criteria for bilinear operators.

Abstract

Commutators of a large class of bilinear operators and multiplication by functions in a certain subspace of the space of functions of bounded mean oscillations are shown to be jointly compact. Under a similar commutation, fractional integral versions of the bilinear Hilbert transform yield separately compact operators.