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

Two-Weight Tb Theorems for Well-Localized Operators