Haagerup's inequality for convolvers on free groups may be interpreted as a result on A1 buildings, i.e. trees. Here are proved analogous inequalities for discrete groups acting freely on the vertices of A1 x A1 and A2 buildings. The results apply in particular to groups of typerotating automorphisms acting simply transitively on the vertices of such buildings. These results provide the first examples of higher rank groups with property (RD).
Ramagge, J., Robertson, A. G. & Steger, T. (1998). A Haagerup inequality for A1 x A1 and A2 buildings. Geometric and Functional Analysis, 8, 702-731.