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Harmonic analysis and BMO-spaces of free Araki--Woods factors

Volume 246 / 2019

Martijn Caspers 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.

Authors

  • Martijn CaspersTU Delft
    EWI/DIAM
    P.O. Box 5031
    2600 GA Delft, The Netherlands
    e-mail

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