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We give a proof of a so-called "local $Tb$" Theorem for singular integralswhose kernels satisfy the standard Calder\'on-Zygmund conditions. The presenttheorem, which extends an earlier result of M. Christ \cite{Ch}, was proved in\cite{AHMTT} for "perfect dyadic" Calder\'on-Zygmund operators. The proof in\cite{AHMTT} essentially carries over to the case considered here, with sometechnical adjustments.

A proof of the local $Tb$ Theorem for standard Calder\'{o}n-Zygmund operators