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<p>The purpose of this paper is to characterize the homogeneous Besov spaces in the Dunkl setting. We utilize a new discrete Calderón reproducing formula, that is, the building blocks are differences of the Dunkl-Poisson kernel which involves both the Euclidean metric and the Dunkl metric. To introduce the Besov spaces in the Dunkl setting, new test functions and distributions are introduced. Also we prove a weak-type discrete Calderón reproducing formula for the Dunkl-Besov spaces and demonstrate the completeness of the Dunkl-Besov spaces. As an application, we study the boundedness of Dunkl-Calderón-Zygmund operators on the Dunkl-Besov spaces.</p>

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Homogeneous Besov Spaces in Dunkl Setting

  • 期刊论文

  • 发表日期：

    2025年12月4日

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  • Mengmeng Dou,
  • Jiashu Zhang

摘要

The purpose of this paper is to characterize the homogeneous Besov spaces in the Dunkl setting. We utilize a new discrete Calderón reproducing formula, that is, the building blocks are differences of the Dunkl-Poisson kernel which involves both the Euclidean metric and the Dunkl metric. To introduce the Besov spaces in the Dunkl setting, new test functions and distributions are introduced. Also we prove a weak-type discrete Calderón reproducing formula for the Dunkl-Besov spaces and demonstrate the completeness of the Dunkl-Besov spaces. As an application, we study the boundedness of Dunkl-Calderón-Zygmund operators on the Dunkl-Besov spaces.