JournalsrmiVol. 27, No. 2pp. 557–584

Pseudo-localisation of singular integrals in LpL^p

  • Tuomas Hytönen

    University of Helsinki, Finland
Pseudo-localisation of singular integrals in $L^p$ cover
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Abstract

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 TfTf has small L2L^2 norm outside a set which only depends on fL2f\in L^2 but not on the arbitrary normalised Calderón-Zygmund operator TT. Parcet also asked if a similar result holds true in LpL^p for p(1,)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 L2L^2 result.

Cite this article

Tuomas Hytönen, Pseudo-localisation of singular integrals in LpL^p. Rev. Mat. Iberoam. 27 (2011), no. 2, pp. 557–584

DOI 10.4171/RMI/646