$(\delta, \gamma)$-Dunkl Lipschitz functions in the space $\mathrm{L}^{2}(\mathbb{R}, |x|^{2\alpha+1}dx)$

  • M. El Hamma University of Hassan II, Km 8 Route d’El Jadida B.P. 5366 Maarif Casablanca 20100, Morocco
  • H. Lahlali University of Hassan II, Km 8 Route d’El Jadida B.P. 5366 Maarif Casablanca 20100, Morocco
  • R. Daher University of Hassan II, Km 8 Route d’El Jadida B.P. 5366 Maarif Casablanca 20100, Morocco
Keywords: Dunkl operator, Dunkl transform, generalized Dunkl translation
Published online: 2014-07-15

Abstract


Using a generalized Dunkl translation, we obtain an analog of Theorem 5.2 in Younis' paper [2] for the Dunkl transform for functions satisfying the $(\delta, \gamma)$-Dunkl Lipschitz condition in the space $\mathrm{L}^{2}(\mathbb{R}, |x|^{2\alpha+1}dx)$.}

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