Pseudo-localisation of singular integrals in L^p

Details Pseudo-localisation of singular integrals in L^p Pseudo-localisation of singular integrals in L^p

2009-09-24

arxiv.org/abs/0909.4481v2

Mathematics

Functional Analysis

24 pages, to appear in Rev. Mat. Iberoam., referee's suggestions implemented to improve presentation

Scientific paper

As a step in developing a non-commutative Calderon-Zygmund theory, J. Parcet (J. Funct. Anal., 2009) 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 Calderon-Zygmund operator T. Parcet also asked if a similar result holds true in L^p for 1 < p < infinity. 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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