Abstract
We show using the Beylkin-Coifman-Rokhlin algorithm in the Haar basis that any singular integral operator can be written as the sum of a bounded operator on $L^p$, $1<p<\infty$, and of a perfect dyadic singular integral operator. This allows to deduce a local $T(b)$ theorem for singular integral operators from the one for perfect dyadic singular integral operators obtained by Hofmann, Muscalu, Tao, Thiele and the first author.
Citation
P. Auscher. Q. X. Yang. "BCR Algorithm and the $T(b)$ Theorem." Publ. Mat. 53 (1) 179 - 196, 2009.
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