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Positivity

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Lipschitz and Triebel–Lizorkin spaces associated with the Dunkl operators on \(\mathbb {R}^d\)

  • Samir KallelEmail author
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Abstract

In this paper we define Lipschitz and Triebel–Lizorkin spaces associated with the differential-difference Dunkl operators on \(\mathbb {R}^d\). We study inclusion relations among them. Next, some interpolation results and continuity results of some important operators (the Dunkl–Poisson semigroup and Dunkl–Flett potentials) on them are established. Also, we prove certain inclusion relations between Dunkl–Sobolev classes \(\mathcal{L}^p_{\alpha ,k}(\mathbb {R}^d)\) of positive fractional order \(\alpha \), Dunkl–Lipschitz spaces \(\wedge ^k_{\alpha ,p,q}(\mathbb {R}^d)\) and Dunkl–Triebel–Lizorkin spaces \(F^k_{\alpha ,p,q}(\mathbb {R}^d)\).

Keywords

Dunkl operators Dunkl–Poisson transforms Dunkl–Lipschitz spaces Dunkl–Triebel–Lizorkin spaces Dunkl–Flett potentials 

Mathematics Subject Classification

26A16 42A38 42B25 

Notes

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Authors and Affiliations

  1. 1.Université Tunis El Manar, Faculté des Sciences de Tunis, Laboratoire d’Analyse Mathématiques et Applications LR11ES11TunisTunisia
  2. 2.Department of Mathematics, Higher Institute of Computer Sciences and Mathematics of MonastirMonastir UniversityMonastirTunisia

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