arXiv:1904.08725 Abstract | arXiv Analytics

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

Published 2019-04-18Version 1

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

Comments: 27 pages

Categories: math.AP, math.FA

Keywords: dunkl operators, application, weighted higher order rellich, nonlinear damped wave equations, classical caffarelli-kohn-nirenberg inequalities

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