作用在树上的群的Fourier乘子的几何描述

Geometric interpretations for Fourier multipliers on groups acting on trees

本文研究一类群上的Fourier乘子的几何描述,以及这些乘子在其群von Neumann代数的非交换L_(p)(1<p<∞)空间上的有界性.这类群为在树上有稳定作用的群.这些作用赋予了群本身某些几何结构,使得我们可以给出群上一些有趣的Fourier乘子.

In this paper,we study Fourier multipliers on groups that admit actions on trees,using a geometric argument.In particular,we obtain the boundedness of the multipliers we construct on the non-commutative L_(p)-spaces(1<p<∞)associated with the group von Neumann algebras.