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<p>In this paper, we investigate multiplier operators associated with the Dunkl transform. By establishing a weighted Littlewood-Paley type theorem for the Dunkl transform, we prove Hörmander’s multiplier theorem for weighted Lebesgue spaces. Furthermore, we demonstrate the boundedness of maximal operators in the Dunkl setting on variable exponent Lebesgue spaces. These results collectively yield Hörmander’s multiplier theorem for Lebesgue spaces with variable exponents. Our approach eliminates the restriction imposed on the space of radial functions, thereby extending the applicability of the theory.</p>

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Dunkl Multipliers in Weighted and Variable Exponent Lebesgue Spaces

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Ziwei Li,
  • Jiman Zhao

摘要

In this paper, we investigate multiplier operators associated with the Dunkl transform. By establishing a weighted Littlewood-Paley type theorem for the Dunkl transform, we prove Hörmander’s multiplier theorem for weighted Lebesgue spaces. Furthermore, we demonstrate the boundedness of maximal operators in the Dunkl setting on variable exponent Lebesgue spaces. These results collectively yield Hörmander’s multiplier theorem for Lebesgue spaces with variable exponents. Our approach eliminates the restriction imposed on the space of radial functions, thereby extending the applicability of the theory.