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