Analysis & Applications Seminar
Proper cocycles, measure equivalence and L_p-Fourier multipliers
Speaker: Simeng Wang (Harbin Institute of Technology)Date: Friday, 16 January 2026 - 11:30Place: Aula 520, Módulo 17, Departamento de Matemáticas, UAM
Abstract:
Various properties of group von Neumann algebras are invariant under measure equivalence, such as the Haagerup property and weak amenability. This fact, as observed by Jolissiant, is based on a certain transference of Fourier-Schur multipliers. We establish a new transference method of completely bounded L_p-Fourier multipliers for proper cocycles for pmp group actions on standard probability spaces. This generalizes the aforementioned results by Jolissaint (and Haagerup et al) which only deals with the case p = ∞. In particular, this gives a natural transference method of Fourier multipliers between groups with measure equivalence, which directly implies and notably generalizes the main result of Hong-Wang-Wang on the pointwise convergence of noncommutative Fourier series on amenable groups. As a second application, this theory also yields a noncommutative Jodiet theorem that transfers L_p-Fourier multipliers from lattices to the ambient group, which strengthens the previous results for Schur multipliers obtained by Haagerup and Lafforgue-de la Salle. Our approach also provides a proper analogue of noncommutative Hilbert transform on SL(2, R) for all 1 < p < ∞. I will also mention the links with de Leeuw restriction problems.
This is joint work with Gan Yao and Runlian Xia.
