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We prove a Bernstein-type inequality invoking a generalized translation operator, closely connected to the generalized Dunkl transform in the one-variable case, \(\mathscr {F}_{k,n}\) . This inequality can be utilized to prove weak-type \((1,1)\) and strong-type \((p,p)\) estimates for multiplier operators.

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A Bernstein-type Inequality for the Generalized Dunkl Translation

  • 会议论文

  • 发表日期：

    2025年

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  • Selma Negzaoui

摘要

We prove a Bernstein-type inequality invoking a generalized translation operator, closely connected to the generalized Dunkl transform in the one-variable case, \(\mathscr {F}_{k,n}\) . This inequality can be utilized to prove weak-type \((1,1)\) and strong-type \((p,p)\) estimates for multiplier operators.