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- W4300794254 abstract "We investigate Fourier multipliers on the compact dual of arbitrary discrete groups. Our main result is a Hormander-Mihlin multiplier theorem for finite-dimensional cocycles with optimal smoothness condition. We also find Littlewood-Paley type inequalities in group von Neumann algebras, prove $L_p$ estimates for noncommutative Riesz transforms and characterize $L_infty to mathrm{BMO}$ 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 Calder'on-Zygmund theory." @default.
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- W4300794254 date "2010-10-26" @default.
- W4300794254 modified "2023-10-18" @default.
- W4300794254 title "Smooth Fourier multipliers on group von Neumann algebras" @default.
- W4300794254 doi "https://doi.org/10.48550/arxiv.1010.5320" @default.
- W4300794254 hasPublicationYear "2010" @default.
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