  Haagerup's inequality for convolvers on free groups may be interpreted as a
result on $\tA_1$ buildings, i.e. trees. Here are proved analogous inequalities
for discrete groups acting freely on the vertices of $\tA_1\times\tA_1$ and
$\tA_2$ buildings. The results apply in particular to groups of type-rotating
automorphisms acting simply transitively on the vertices of such buildings.
These results provide the first examples of higher rank groups with property
(RD).
