Pseudo-localization of singular integrals and noncommutative Calderon-Zygmund theory
Classical Analysis and ODEs
2007-05-23 v1 Operator Algebras
Abstract
In this paper we obtain the weak type (1,1) boundedness of Calderon-Zygmund operators acting over operator-valued functions. Our main tools for its solution are a noncommutative form of Calderon-Zygmund decomposition in conjunction with a pseudo-localization principle for singular integrals, which is new even in the classical setting and of independent interest. Perhaps because of the hidden role of pseudo-localization and almost orthogonality, this problem has remained open for quite some time. We also consider Calderon-Zygmund operators associated to certain operator-valued kernels.
Keywords
Cite
@article{arxiv.0704.2950,
title = {Pseudo-localization of singular integrals and noncommutative Calderon-Zygmund theory},
author = {Javier Parcet},
journal= {arXiv preprint arXiv:0704.2950},
year = {2007}
}
Comments
72 pages, 6 figures