On the boundedness of Dunkl multipliers

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 Lᵖ boundedly into Lᵖ for all p ≥ 2.