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Mathematische Annalen

, Volume 352, Issue 3, pp 691–743 | Cite as

BMO spaces associated with semigroups of operators

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Abstract

We study BMO spaces associated with semigroup of operators on noncommutative function spaces (i.e. von Neumann algebras) and apply the results to boundedness of Fourier multipliers on non-abelian discrete groups. We prove an interpolation theorem for BMO spaces and prove the boundedness of a class of Fourier multipliers on noncommutative L p spaces for all 1 < p < ∞, with optimal constants in p.

Mathematics Subject Classification (2000)

46L51 (42B25 46L10 47D06) 
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© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA
  2. 2.Department of MathematicsWayne state UniversityDetroitUSA

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