A T(L) theorem for the Calder\'{o}n--Zygmund operators in BMO($\mathbb{R}^d$)

TL;DR

This paper develops a new criterion for characterizing bounded Calderón--Zygmund operators on BMO spaces, extending classical results and applying them to Calderón commutators.

Contribution

It introduces a T(L) theorem variant for BMO spaces, providing a novel characterization of Calderón--Zygmund operators and their boundedness.

Findings

Established a T(L) theorem for BMO($\mathbb{R}^d$)

Characterized bounded Calderón--Zygmund operators on BMO

Applied the criterion to Calderón commutators

Abstract

A variant of the global $T(1)$ criterion to characterize the bounded Calder\'{o}n--Zygmund operators on BMO($\mathbb{R}^d$) is proved. We apply it to the certain Calder\'on commutators.