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Characterization of Function Spaces for the Dunkl Type Operator on the Real Line

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Abstract

In this work we consider the Dunkl operator on the real line, defined by

$$ {\cal D}_kf(x):=f'(x)+k\dfrac{f(x)-f(-x)}{x},\,\,k\geq0. $$

We define and study Dunkl–Sobolev spaces \(L^p_{n,k}(\mathbb{R})\), Dunkl–Sobolev spaces \({\cal L}^p_{\alpha,k}(\mathbb{R})\) of positive fractional order and generalized Dunkl–Lipschitz spaces \(\wedge^k_{\alpha,p,q}(\mathbb{R})\). We provide characterizations of these spaces and we give some connection between them.

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  1. Department of Mathematics, Faculty of Sciences of Tunis, University Campus, 2092, Tunis, Tunisia

    Samir Kallel

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  1. Samir Kallel
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Kallel, S. Characterization of Function Spaces for the Dunkl Type Operator on the Real Line. Potential Anal 41, 143–169 (2014). https://doi.org/10.1007/s11118-013-9366-5

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