Two Weight Bump Conditions for Compactness of Commutators

TL;DR

This paper establishes new two weight bump conditions that are sufficient for the compactness of commutators involving Calderón-Zygmund operators, advancing understanding in the two weight setting without extra assumptions.

Contribution

It introduces the first two weight bump conditions guaranteeing compactness of commutators without additional weight restrictions.

Findings

Two weight bump conditions are sufficient for compactness.

First result for compactness in two weight setting without extra assumptions.

Advances the theory of commutator compactness in harmonic analysis.

Abstract

We prove certain two weight bump conditions are sufficient for the compactness of the commutator $[b,T]$ where $b\in CMO$ and $T$ is a Calder\'on- Zygmund operator. This is the first result for compactness in the two weight setting without additional assumptions on the individual weights.