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<p>This research is devoted to the study of the weighted integrability of <i>q</i>-Dunkl transforms under certain sufficient and necessary conditions in terms of the moduli of smoothness connected with <i>q</i>-Dunkl translation operators. These results are inspired by a Móricz-type result in classical Fourier analysis, which generalizes the well-known Titchmarsh conditions for functions from Lipschitz classes. Some further results on the integrability of the <i>q</i>-Dunkl transform of <i>q</i>-Dunkl convolutions are also given.</p>

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On the weighted integrability of q-Dunkl transforms

  • 期刊论文

  • 发表日期：

    2025年7月31日

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  • Othman Tyr

摘要

This research is devoted to the study of the weighted integrability of q-Dunkl transforms under certain sufficient and necessary conditions in terms of the moduli of smoothness connected with q-Dunkl translation operators. These results are inspired by a Móricz-type result in classical Fourier analysis, which generalizes the well-known Titchmarsh conditions for functions from Lipschitz classes. Some further results on the integrability of the q-Dunkl transform of q-Dunkl convolutions are also given.