  In this article we use Littlewood-Paley-Stein theory to prove two versions of
Dunkl multiplier theorem when the multiplier $ m $ satisfies a modified
H\"ormander condition. When $ m $ is radial we give a simple proof of a known
result. For general $ m $ we prove that the Dunkl multiplier operator takes
radial functions in $ L^p $ boundedly into $ L^p $ for all $ p \geq 2.$
