  Normal elements (or multipliers) of the C* algebra of a certain class of
locally compact groupoids admit a natural faithful representation as normal
operators on the $L^2$-space of a dense orbit of the groupoid. We prove norm
estimates on the product between elements of the functional calculus of these
operators and multiplication operators, subject to suitable restrictions
expressed in terms of the orbit structure of the groupoid. As a consequence,
one gets uniform estimates on the local behavior of the evolution group of the
operators.
