We prove a Hörmander-type spectral multiplier theorem for a sublaplacian on SU(2), with critical index determined by the
Euclidean dimension of the group. This result is the analogue for SU(2) of the result for the Heisenberg group obtained by
D. Müller and E.M. Stein and by W. Hebisch.
Mathematics Subject Classification (1991):42B15, 35P99
Received March 7, 2000; in final form April 11, 2000 / Published online April 12, 2001