Abstract
We study Fourier multipliers of Hilbert transform type on free groups. We prove that they are completely bounded on noncommutative -spaces associated with the free group von Neumann algebras for all . This implies that the decomposition of the free group into reduced words starting with distinct free generators is completely unconditional in . We study the case of Voiculescu’s amalgamated free products of von Neumann algebras as well. As by-products, we obtain a positive answer to a compactness problem posed by Ozawa, a length-independent estimate for Junge–Parcet–Xu’s free Rosenthal’s inequality, a Littlewood–Paley–Stein-type inequality for geodesic paths of free groups, and a length reduction formula for -norms of free group von Neumann algebras.
Citation
Tao Mei. Éric Ricard. "Free Hilbert transforms." Duke Math. J. 166 (11) 2153 - 2182, 15 August 2017. https://doi.org/10.1215/00127094-2017-0007
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