Duke Mathematical Journal
- Duke Math. J.
- Volume 166, Number 11 (2017), 2153-2182.
Free Hilbert transforms
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.
Duke Math. J., Volume 166, Number 11 (2017), 2153-2182.
Received: 5 July 2016
Revised: 10 February 2017
First available in Project Euclid: 28 April 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Mei, Tao; Ricard, Éric. Free Hilbert transforms. Duke Math. J. 166 (2017), no. 11, 2153--2182. doi:10.1215/00127094-2017-0007. https://projecteuclid.org/euclid.dmj/1493344841