Convolution operators and Bochner-Riesz means on Herz-type Hardy spaces in the Dunkl setting
For \(T\in \mathcal{S}'(\mathbb{R})\) and \(f\in \mathcal{S}(\mathbb{R})\), the Dunkl convolution product \(T\ast_{\alpha}f\) is defined by \[ T\ast_{\alpha}f(x)=\langle T(y), \tau_x f(-y)\rangle,\quad x\in \mathbb{R}, \] where \(\tau_x\) is the Dunkl translation operator. The author investigates the Dunkl convolution operators on Herz-type Hardy spaces \(\mathcal{H}_{\alpha,2}^{p}\) and establishes a version of multiplier theorem for the maximal Bochner-Riesz operators on the Herz-type Hardy spaces \(\mathcal{H}_{\alpha,\infty}^{p}\). Some related results are contained in the paper by \textit{S. Lu} and \textit{D. Yang} [Proc. Am. Math. Soc. 126, No.~11, 3337--3346 (1998; Zbl 0905.42007)].
scientific article; zbMATH DE number 5847811