Weighted Dunkl transform inequalities and application on radial Besov spaces |
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Authors: | Chokri Abdelkefi Abdessattar Jemai |
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Institution: | 1. Department of Mathematics, Preparatory Institute of Engineer Studies of Tunis, 1089 Monfleury, University of Tunis, Tunis, Tunisia
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Abstract: | In Dunkl theory on $\mathbb R ^d$ which generalizes classical Fourier analysis, we prove first weighted inequalities for certain Hardy-type averaging operators. In particular, we deduce for specific choices of the weights the $d$ -dimensional Hardy inequalities whose constants are sharp and independent of $d$ . Second, we use the weight characterization of the Hardy operator to prove weighted Dunkl transform inequalities. As consequence, we obtain Pitt’s inequality which gives an integrability theorem for this transform on radial Besov spaces. |
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