Rellich, Gagliardo—Nirenberg, Trudinger and Caffarelli—Kohn—Nirenberg inequalities for Dunkl operators and applications

In this paper we introduce several extended versions of the classical Caffarelli—Kohn—Nirenberg inequalities. Moreover, obtain weighted higher order Rellich, Gagliardo—Nirenberg, Caffarelli—Kohn—Nirenberg, Trudinger inequalities and uncertainty principle for Dunkl operators. Furthermore, give an application Gagliardo—Nirenberg inequality to Cauchy problem nonlinear damped wave equations Laplacian.