We establish fractional Leibniz rules for the Dunkl Laplacian \(\Delta _k\) of the form \(\begin{aligned}&\Vert (-\Delta _k)^s(fg)\Vert _{L^p(d\mu _k)} \lesssim \Vert (-\Delta _k)^s f\Vert _{L^{p_1}(d\mu _k)} \Vert g\Vert _{L^{p_2}(d\mu _k)}\\&+ \Vert f\Vert _{L^{p_1}(d\mu _k)} \Vert (-\Delta _k)^s g\Vert _{L^{p_2}(d\mu _k)}. \end{aligned}\) Our approach relies on adapting the classical paraproduct decomposition to the Dunkl setting. In the process, we develop several new auxiliary results. Specifically, we show that for a Schwartz function f, the function \((-\Delta _k)^s f\) satisfies a pointwise decay estimate; we establish a version of almost orthogonality estimates adapted to the Dunkl framework; and we investigate the boundedness of Dunkl paraproduct operators on the Lebesgue spaces.
