Dunkl paraproducts and fractional Leibniz rules for the Dunkl Laplacian

The Anh Bui, Suman Mukherjee

We establish fractional Leibniz rules for the Dunkl Laplacian ${\Delta }_k$ of the form $$\|(-Δ_k)^s(fg)\|_{L^p(dμ_k)} \lesssim \|(-Δ_k)^s f\|_{L^{p_1}(dμ_k)} \|g\|_{L^{p_2}(dμ_k)} + \|f\|…