Weak boundedness of Calderón-Zygmund operators on noncommutative \(L_1\)-spaces

In 2008, J. Parcet showed the \((1,1)\) weak-boundedness of Calderón-Zygmund operators acting on functions taking values in a von Neumann algebra. We propose a simplified version of his proof using the same tools : Cuculescu's projections and a pseudo-localisation theorem. This will unable us t...

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Bibliographic Details
Published in:arXiv.org 2017-11
Main Author: Léonard Cadilhac
Format: Article
Language:English
Subjects:
Localization
Mathematical analysis
Operators (mathematics)
Online Access:Get full text
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Summary:In 2008, J. Parcet showed the \((1,1)\) weak-boundedness of Calderón-Zygmund operators acting on functions taking values in a von Neumann algebra. We propose a simplified version of his proof using the same tools : Cuculescu's projections and a pseudo-localisation theorem. This will unable us to recover the \(L_p\)-boundedness of Calderón-Zygmund operators with Hilbert valued kernels acting on operator valued functions for \(1 < p < \infty\) and an \(L_p\)-pseudo-localisation result of P. Hyt\"onen.
ISSN:2331-8422