On operator norms for hyperbolic groups

TL;DR

This paper investigates the operator norms of radial functions on hyperbolic groups, demonstrating the optimality of various forms of Haagerup's inequality through precise estimates.

Contribution

It provides new bounds for operator norms on hyperbolic groups and establishes the optimality of certain inequalities, advancing understanding in geometric group theory.

Findings

Operator norm estimates for radial functions on hyperbolic groups

Proof of optimality for several forms of Haagerup's inequality

Enhanced understanding of harmonic analysis on hyperbolic groups

Abstract

We estimate the operator norm of radial non-negative functions on hyperbolic groups. As a consequence, we show that several forms of Haagerup's inequality are optimal.