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BCR algorithm and the \(T(b)\) theorem. (English) Zbl 1153.42003

Summary: 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 S. Hofmann, C. Muscalu, T. Tao, C. Thiele and the first author [Publ. Mat., Barc. 46, No. 2, 257–325 (2002; Zbl 1027.42009)].

MSC:

42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems

Citations:

Zbl 1027.42009
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