Dimension free weak-type endpoint estimates for the vectors of the Dunkl--Riesz transform

Let $R\subset\mathbb{R}^d$ be a reduced root system, $G$ the associated finite reflection group, and $k\ge0$ a $G$-invariant multiplicity function. We develop a Dunkl analogue of the obstacle/partial-balayage method of Ouyang, Spector, and Stockdale (https://arxiv.org/abs/2608.18068) for the Euclide