Pseudo-localisation of singular integrals in

  • Tuomas Hytönen

    University of Helsinki, Finland


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 has small norm outside a set which only depends on but not on the arbitrary normalised Calderón-Zygmund operator . Parcet also asked if a similar result holds true in for . This is answered in the affirmative in the present paper. The proof, which is based on martingale techniques, even somewhat improves on the original result.

Cite this article

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

DOI 10.4171/RMI/646