Pri: 35L05. Sec: 22E30.

We define the Littlewood-Paley decomposition associated with the Dunkl operators; from this decomposition we give the characterization of the Sobolev, Hölder and Lebesgue spaces associated with the Dunkl operators. We construct the paraproduct operators associated with the Dunkl operators similar to those defined by J.M. Bony in [1]. Using the Littlewood-Paley decomposition we establish the Sobolev embedding, Gagliardo-Nirenberg inequality and we present the paraproduct algorithm.;