For the Dunkl transforms associated with the weight functions $$h_{\kappa }^2(x)=\prod _{j=1}^d |x_j|^{2{\kappa }_j}$$ , $${\kappa }_1,\ldots , {\kappa }_d\ge 0$$ on $${{\mathbb {R}}}^d$$ , it is proved that if $$p\ge 2$$ and $${\delta }>{\delta }_{\kappa }(p):=\max \{(2l_{\kappa }+1) |\frac{1}{2}-\frac{1}{p}|-\frac{1}{2},0\}$$ , the Bochner–Riesz means $$B_{R}^{\delta }(h_{\kappa }^2; f)$$ converges to f at almost everywhere for all $$f\in L^p({{\mathbb {R}}}^d; h_{\kappa }^2dx)$$ . This extends a well known result of Carbery et al. for the classical Fourier transforms (J Lond Math Soc 38:513–524, 1988).

中文翻译：

---

对于加权 $$L^{p}$$Lp 函数的 Dunkl 变换，Bochner-Riesz 几乎处处收敛意味着

对于与权重函数相关的 Dunkl 变换 $$h_{\kappa }^2(x)=\prod _{j=1}^d |x_j|^{2{\kappa }_j}$$ , $${ \kappa }_1,\ldots , {\kappa }_d\ge 0$$ on $${{\mathbb {R}}}^d$$ ，证明如果 $$p\ge 2$$ 和 $ ${\delta }>{\delta }_{\kappa }(p):=\max \{(2l_{\kappa }+1) |\frac{1}{2}-\frac{1}{p }|-\frac{1}{2},0\}$$ ，Bochner-Riesz 的意思是 $$B_{R}^{\delta }(h_{\kappa }^2; f)$$ 收敛到 f对于所有 $$f\in L^p({{\mathbb {R}}}^d; h_{\kappa }^2dx)$$ 几乎无处不在。这扩展了 Carbery 等人的众所周知的结果。用于经典傅立叶变换 (J Lond Math Soc 38:513–524, 1988)。