Weak boundedness of Calderón-Zygmund operators on noncommutative L₁-spaces

2017/02/21 by Cadilhac, Léonard · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1702.06536

Abstract

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 < ∞ and an L_p-pseudo-localisation result of P. Hytönen.

Cited by

• Noncommutative weak type (1,1) estimates for Calderón-Zygmund operators with a class of L₁-integral conditions

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