Weyl multipliers for invariant Sobolev spaces

A concrete characterization for the Lp-multipliers (1 < p < ∞) for the Weyl transform is obtained. This is used to study the Weyl multipliers for Laguerre Sobolev spaces Wm,p (ℂn). A dual space characterization is obtained for the Weyl multiplier class MW(Wm,lL (ℂn)).