# Two-Weight Tb Theorems for Well-Localized Operators

## TL;DR

This paper introduces new two-weight Tb theorems for well-localized operators, expanding the theoretical framework for analyzing such operators with respect to pairs of accretive functions and systems.

## Contribution

It establishes both global and local two-weight Tb theorems for well-localized operators, combining recent proof techniques with classical T1 theorem methods.

## Key findings

- Proved a global two-weight Tb theorem for well-localized operators.
- Established a local two-weight Tb theorem for operators with respect to accretive systems.
- Integrated recent Tb proof techniques with classical T1 theorem arguments.

## Abstract

This paper first defines operators that are "well-localized" with respect to a pair of accretive functions and establishes a global two-weight Tb theorem for such operators. Then it defines operators that are "well-localized" with respect to a pair of accretive systems and establishes a local two-weight Tb theorem for them. The proofs combine recent Tb proof techniques with arguments used to prove earlier T1 theorems for well-localized operators.