Pseudo-localisation of singular integrals in L^p
Functional Analysis
2010-04-15 v2 Classical Analysis and ODEs
Abstract
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.
Keywords
Cite
@article{arxiv.0909.4481,
title = {Pseudo-localisation of singular integrals in L^p},
author = {Tuomas P. Hytönen},
journal= {arXiv preprint arXiv:0909.4481},
year = {2010}
}
Comments
24 pages, to appear in Rev. Mat. Iberoam., referee's suggestions implemented to improve presentation