Commutators of singular integrals revisited

TL;DR

This paper characterizes the two-weighted boundedness of iterated commutators of singular integrals, offering new insights even in unweighted cases, and broadens understanding of operator boundedness conditions.

Contribution

It provides a Bloom-type characterization for two-weighted boundedness of iterated commutators, including the first such result in the unweighted setting.

Findings

Established necessity for a wide class of operators.

Extended Bloom-type characterization to iterated commutators.

First unweighted setting result for first order commutators.

Abstract

We obtain a Bloom-type characterization of the two-weighted boundedness of iterated commutators of singular integrals. The necessity is established for a rather wide class of operators, providing a new result even in the unweighted setting for the first order commutators.