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May, 2011 Pseudo-localisation of singular integrals in $L^p$
Tuomas P. Hytönen
Rev. Mat. Iberoamericana 27(2): 557-584 (May, 2011).


As a step in developing a non-commutative Calderón-Zygmund theory, J. Parcet (J. Funct. Anal. {\bf 256} (2009), no. 2, 509-593) established a new pseudo-localisation principle for classical singular integrals, showing that $Tf$ has small $L^2$ norm outside a set which only depends on $f\in L^2$ but not on the arbitrary normalised Calderón-Zygmund operator $T$. Parcet also asked if a similar result holds true in $L^p$ for $p\in(1,\infty)$. This is answered in the affirmative in the present paper. The proof, which is based on martingale techniques, even somewhat improves on the original $L^2$ result.


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Tuomas P. Hytönen . "Pseudo-localisation of singular integrals in $L^p$." Rev. Mat. Iberoamericana 27 (2) 557 - 584, May, 2011.


Published: May, 2011
First available in Project Euclid: 10 June 2011

zbMATH: 1223.42010
MathSciNet: MR2848530

Primary: 42B20 , 60G46

Keywords: $T(1)$ theorem , Calderón-Zygmund operator , operations on the Haar basis

Rights: Copyright © 2011 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.27 • No. 2 • May, 2011
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