Weighted Function Spaces and Dunkl Transform |
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Authors: | Chokri Abdelkefi |
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Institution: | 1. Department of Mathematics, Preparatory Institute of Engineer Studies of Tunis, University of Tunis, 1089, Monfleury Tunis, Tunisia
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Abstract: | We introduce first weighted function spaces on ${\mathbb{R}^d}$ using the Dunkl convolution that we call Besov-Dunkl spaces. We provide characterizations of these spaces by decomposition of functions. Next we obtain in the real line and in radial case on ${\mathbb{R}^d}$ weighted L p -estimates of the Dunkl transform of a function in terms of an integral modulus of continuity which gives a quantitative form of the Riemann-Lebesgue lemma. Finally, we show in both cases that the Dunkl transform of a function is in L 1 when this function belongs to a suitable Besov-Dunkl space. |
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