Tue, 07 Mar 2023
Runlian Xia
University of Glasgow

The Hilbert transform H is a basic example of a Fourier multiplier, and Riesz proved that H is a bounded operator on Lp(T) for all p between 1 and infinity.  We study Hilbert transform type Fourier multipliers on group algebras and their boundedness on corresponding non-commutative Lp spaces. The pioneering work in this direction is due to Mei and Ricard who proved Lp-boundedness of Hilbert transforms on free group von Neumann algebras using a Cotlar identity. In this talk, we introduce a generalised Cotlar identity and a new geometric form of Hilbert transform for groups acting on tree-like structures. This class of groups includes amalgamated free products, HNN extensions, left orderable groups and many others.  This is joint work with Adrián González and Javier Parcet.

Please contact us with feedback and comments about this page. Last updated on 01 Mar 2023 16:44.