Smooth Fourier multipliers on group von Neumann algebras
By Marius Junge, Tao Mei, Javier Parcet. 2010
110 citations recorded by the source corpus.
We investigate Fourier multipliers on the compact dual of arbitrary discrete groups. Our main result is a Hörmander–Mihlin multiplier theorem for finite-dimensional cocycles with optimal smoothness condition. We also find Littlewood–Paley type inequalities in group von Neumann algebras, prove Lp estimates for noncommutative Riesz transforms and characterize L∞ → BMO boundedness for radial Fourier multipliers. The key novelties of our approach are to exploit group cocycles and cross products in Fourier multiplier theory in conjunction with BMO spaces associated to semigroups of operators and a noncommutative generalization of Calderón–Zygmund theory.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c4caa7a98f7ee58ba1c3f77d468a28da12055a3a
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In Applied Mathematics
- Javier Parcet
- Marius Junge
- A. Gonz'alez-P'erez
- Quanhua Xu
- Narcisse Randrianantoanina
- Tao Mei
- Sjoerd Dirksen
- Uffe Haagerup
In Mathematical Physics
- Javier Parcet
- Marius Junge
- A. Gonz'alez-P'erez
- Quanhua Xu
- Narcisse Randrianantoanina
- Tao Mei
- Sjoerd Dirksen
- Gilles Pisier
Citations in the corpus
- Noncommutative martingale deviation and Poincaré type inequalities with applications (2012, unknown): “We recall the definition following [27].”
- Singular integrals in quantum Euclidean spaces (2017, methodology): “ng by left/right or Schur multiplication, other BMO spaces in a new approach towards nondoubling CZ theory, Littlewood-Paley estimates, Ho¨rmander-Mihlin multipliers or directional Hilbert transforms [15, 16, 37, 42, 54]. The Caldero´n-Zygmund theory presented below is the first form over a ‘fully no”