Harmonic analysis and BMO-spaces of free Araki-Woods factors
Abstract
We consider semi-group 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∞ → BMO multipliers. We also provide Lp-bounds for a natural generalization of the Hilbert transform.
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