Publicacions Matemàtiques

BCR Algorithm and the $T(b)$ Theorem

P. Auscher and Q. X. Yang

Full-text: Open access

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.

Article information

Source
Publ. Mat., Volume 53, Number 1 (2009), 179-196.

Dates
First available in Project Euclid: 17 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.pm/1229531049

Mathematical Reviews number (MathSciNet)
MR2474120

Zentralblatt MATH identifier
1153.42003

Subjects
Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42C40: Wavelets and other special systems

Keywords
Singular integral operators Haar basis

Citation

Auscher, P.; Yang, Q. X. BCR Algorithm and the $T(b)$ Theorem. Publ. Mat. 53 (2009), no. 1, 179--196. https://projecteuclid.org/euclid.pm/1229531049


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