Weighted norm inequalities of Bochner–Riesz means

Let w be a Muckenhoupt weight and be the weighted Hardy spaces. We use the atomic decomposition of and their molecular characters to show that the Bochner–Riesz means are bounded on for 0max{n/p−(n+1)/2,[n/p]rw−1(rw−1)−(n+1)/2}, where rw is the critical index of w for the reverse Hölder condition. We also prove the boundedness of the maximal Bochner–Riesz means for 0n/p−(n+1)/2.