Harmonic analysis and BMO-spaces of free Araki--Woods factors
Volume 246 / 2019
Studia Mathematica 246 (2019), 71-107
MSC: Primary 47A20, 47A57, 47D07.
DOI: 10.4064/sm170904-14-1
Published online: 13 September 2018
Abstract
We consider semigroup BMO-spaces associated with arbitrary von Neumann algebras and prove interpolation theorems. This extends results by Junge–Mei for the tracial case. We give examples of multipliers on free Araki–Woods algebras and in particular we find $L_\infty \rightarrow {\rm BMO}$ multipliers. We also provide $L_p$-bounds for a natural generalization of the Hilbert transform.
