Boundedness results for commutators with BMO functions via weighted estimates: a comprehensive approach

TL;DR

This paper introduces a unified method for deriving weighted estimates of commutators with BMO functions, applicable to various operators and settings, recovering known results and establishing new ones.

Contribution

A comprehensive approach that extends weighted estimates for commutators with BMO functions to a broad range of operators and contexts, including new results.

Findings

Recovered many known weighted estimates for commutators.

Established new weighted bounds for multilinear commutators.

Demonstrated the versatility of the Cauchy integral trick in this setting.

Abstract

We present a unified method to obtain weighted estimates of linear and multilinear commutators with BMO functions, that is amenable to a plethora of operators and functional settings. Our approach elaborates on a commonly used Cauchy integral trick, recovering many known results but yielding also numerous new ones.