Generalized Lorentz Spaces and Applications

We define and study the Lorentz spaces associated with the Dunkl operators onℝd. Furthermore, we obtain the Strichartz estimates for the Dunkl-Schrödinger equations under the generalized Lorentz norms. The Sobolev inequalities between the homogeneous Dunkl-Besov spaces and generalized Lorentz spaces are also considered.