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

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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 \(F^k_{\alpha ,p,q}(\mathbb {R}^d)\).

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Authors and Affiliations

  1. Université Tunis El Manar, Faculté des Sciences de Tunis, Laboratoire d’Analyse Mathématiques et Applications LR11ES11, 2092, El Manar I, Tunis, Tunisia

    Samir Kallel

  2. Department of Mathematics, Higher Institute of Computer Sciences and Mathematics of Monastir, Monastir University, 5000, Monastir, Tunisia

    Samir Kallel

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  1. Samir Kallel
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Kallel, S. Lipschitz and Triebel–Lizorkin spaces associated with the Dunkl operators on \(\mathbb {R}^d\). Positivity 23, 1021–1049 (2019). https://doi.org/10.1007/s11117-019-00650-y

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