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<p>We establish the weak (1, 1) boundedness of the Littlewood–Paley–Stein square function associated with the Dunkl heat flow, which is generated by the non-local Dunkl Laplacian. Our proof relies on precise integral estimates for derivatives of the Dunkl heat kernel, combined with the technique of Caldrón–Zygmund decomposition. This is the continuity of the recent work [Math. Nachr. 296: 1225–1243 (2023)], where dimension-free <i>L</i><sup><i>p</i></sup> boundedness for the same square functions was proved.</p>

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Weak Type Estimates for Square Functions of Dunkl Heat Flows

  • 期刊论文

  • 发表日期：

    2025年5月29日

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  • Huaiqian Li

摘要

We establish the weak (1, 1) boundedness of the Littlewood–Paley–Stein square function associated with the Dunkl heat flow, which is generated by the non-local Dunkl Laplacian. Our proof relies on precise integral estimates for derivatives of the Dunkl heat kernel, combined with the technique of Caldrón–Zygmund decomposition. This is the continuity of the recent work [Math. Nachr. 296: 1225–1243 (2023)], where dimension-free Lp boundedness for the same square functions was proved.