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

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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 L → BMO multipliers. We also provide Lp-bounds for a natural generalization of the Hilbert transform.

Original languageEnglish
Pages (from-to)71-107
Number of pages37
JournalStudia Mathematica
Volume246
Issue number1
DOIs
Publication statusPublished - 2019

Keywords

  • BMO-spaces
  • Complex interpolation
  • Fourier multipliers
  • Free Gaussians
  • Markov semigroups
  • Noncommutative L-spaces

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