Rellich, Gagliardo—Nirenberg, Trudinger and Caffarelli—Kohn—Nirenberg inequalities for Dunkl operators and applications
Velicu A. Yessirkegenov N.
April 2022Hebrew University Magnes Press
Israel Journal of Mathematics
2022#247Issue 2741 - 782 pp.
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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Department of Mathematics, Imperial College London Huxley Building, 180 Queen’s Gate, London, SW7 2AZ, United Kingdom
Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118 route de Narbonne, Toulouse, 31062, France
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, 281 Krijgslaan, Building S8, Ghent, Belgium
Suleyman Demirel University, Kaskelen, Kazakhstan
Institute of Mathematics and Mathematical Modeling, 125 Pushkin str., Almaty, 050010, Kazakhstan
Department of Mathematics
Institut de Mathématiques de Toulouse
Department of Mathematics: Analysis
Suleyman Demirel University
Institute of Mathematics and Mathematical Modeling
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