Two‐weight Tb theorems for well‐localized operators

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.