Weighted norm inequalities of Bochner-Riesz means

Let w be a Muckenhoupt weight and H_w^p (Rⁿ) be the weighted Hardy spaces. We use the atomic decomposition of H_w^p (Rⁿ) and their molecular characters to show that the Bochner-Riesz means T_R^δ are bounded on H_w^p (Rⁿ) for 0 < p ≤ 1 and δ > max {n / p - (n + 1) / 2, [n / p] r_w (r_w - 1)^-1 - (n + 1) / 2}, where r_w is the critical index of w for the reverse Hölder condition. We also prove the H_w^p - L_w^p boundedness of the maximal Bochner-Riesz means T_*^δ for 0 < p ≤ 1 and δ > n / p - (n + 1) / 2.