报告题目：Hilbert Transforms for Groups Acting on Tree-Like Structures
报告时间：2022-11-11 17:00 - 18:00
报告人：Prof.Adrián González Pérez 马德里自治大学 UAM
ZOOMID：885 517 8417 密码：whu2022
Abstract：The Hilbert transform in R is a classical example of a Fourier multiplier. Its boundedness on Lp was proved by Riesz. In the 50s, Cotlar managed, via a recurrence relation, to prove its boundedness without using the theory of singular integrals. More recently, Mei and Ricard generalized the Cotlar identity in order to prove the Lp -boundedness of Hilbert transforms over free products with a similar recurrence relation. In this talk, we will present a Cotlar identity for general group algebras and provide a model of Hilbert transforms satisfying such identity coming from actions on R-trees. Such a model provides non-trivially transforms when the action doesn't have fixed points. Examples of such groups include amalgamated free products, totally ordered groups and HNN extensions among others.
