Translator Disclaimer
15 August 2017 Free Hilbert transforms
Tao Mei, Éric Ricard
Duke Math. J. 166(11): 2153-2182 (15 August 2017). DOI: 10.1215/00127094-2017-0007

Abstract

We study Fourier multipliers of Hilbert transform type on free groups. We prove that they are completely bounded on noncommutative Lp-spaces associated with the free group von Neumann algebras for all 1<p<. This implies that the decomposition of the free group F into reduced words starting with distinct free generators is completely unconditional in Lp. 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 Lp-norms of free group von Neumann algebras.

Citation

Download 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

Information

Received: 5 July 2016; Revised: 10 February 2017; Published: 15 August 2017
First available in Project Euclid: 28 April 2017

zbMATH: 1385.46040
MathSciNet: MR3694567
Digital Object Identifier: 10.1215/00127094-2017-0007

Subjects:
Primary: 46L07
Secondary: 46L52 , 46L54

Keywords: free group , Hilbert transforms , noncommutative $L^{p}$-spaces , von Neumann algebra

Rights: Copyright © 2017 Duke University Press

JOURNAL ARTICLE
30 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.166 • No. 11 • 15 August 2017
Back to Top