BCR algorithm and the T(b) Theorem

BCR algorithm and the T(b) Theorem

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 Lp, 1 < p < ∞, and of a perfect dyadic singular integral operator. This allows to deduce a local T(b) theorem for singular integral opera...

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Veröffentlicht in:Publicacions matemàtiques 2009, Vol.53 (1), p.179-196
Hauptverfasser: Auscher, Pascal, Yang, Q. X.
Format: Artikel
Sprache:eng
Schlagworte:
42B20
42C40
Adjoints
Cauchy Schwarz inequality
Coefficients
Cubes
Dyadics
Haar basis
Mathematical functions
Mathematical integrals
Mathematical theorems
Singular integral operators
Urelements
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Zusammenfassung: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 Lp, 1 < p < ∞, 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.
ISSN:0214-1493
2014-4350
DOI:10.5565/PUBLMAT_53109_08