WEAK BOUNDEDNESS OF OPERATOR-VALUED BOCHNER-RIESZ MEANS FOR THE DUNKL TRANSFORM

We consider operator-valued Bochner-Riesz means with weight function h(k)(2) under a finite reflection group for the Dunkl transform. We establish the maximal inequality of the weighted Hardy-Littlewood maximal function, and we apply it to the maximal inequality of operator-valued Bochner-Riesz means B-R(delta) (h(k)(2); f) (x) for delta > lambda(k) := d-1/2 + Sigma(d)(j-1) k(j). Furthermore, we also obtain the corresponding pointwise convergence theorem.