  In this paper we prove weighted norm inequalities for Weyl multipliers
satisfying Mauceri's condition. As applications of this we obtain some
estimates for $L^p$ multipliers on the Heisenberg group and also show in the
context of a theorem of Weis on operator valued Fourier multipliers that the
R-boundedness of the derivative of the multiplier is not necessary for the
boundedness of the multiplier transform.
