Pseudo-localisation of Singular Integrals in L

Abstract. As a step in developing a non-commutative Calderón–Zygmund theory, J. Parcet (J. Funct. Anal., 2009) established a new pseudo-localisation principle for classical singular integrals, showing that Tf has small L norm outside a set which only depends on f ∈ L but not on the arbitrary normalised Calderón–Zygmund operator T . Parcet also asked if a similar result holds true in L for p ∈ (1,∞). 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 result.