SEMINARIO ANÁLISIS Y APLICACIONES

A cocycle transference method for Lp-Fourier multipliers on group von Neumann algebras

Ponente: Simeng Wang (Harbin Institute of Technology)

Fecha: Miércoles, 21 de junio de 2023 - 10:00

Lugar: Aula Gris 3, ICMAT

Resumen:

We establish a transference method of completely bounded Lp-Fourier multipliers for proper cocycles for pmp group actions on standard probability spaces. This generalizes the previous results by Haagerup and Jolissaint, which only deals with the case p=infty. In particular, this gives a natural transference method of Fourier multipliers between groups with measure equivalence, which yields an easy proof of the main result of Hong-Wang-Wang on the pointwise convergence of noncommutative Fourier series on amenable groups. As a second application, this also yields a transference method of Lp-Fourier multipliers from lattices in a linear Lie group to the whole group, which strengthens the previous results for Schur multipliers obtained by Haagerup and Lafforgue-de la Salle. This is ongoing joint work with Gan Yao.