Weighted norm inequalities of Bochner-Riesz means

Let w be a Muckenhoupt weight and H-w(p)(R-n) be the weighted Hardy spaces. We use the atomic decomposition of H-w(p)(R-n) and their molecular characters to show that the Bochner-Riesz means T-R(delta) are bounded on H-w(p)(R-n) for 0 < p <= 1 and delta > 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 Holder condition. We also prove the H-w(p) - L-w(p) boundedness of the maximal Bochner-Riesz means T-*(delta) for 0 < p <= 1 and delta > n/p - (n + 1)/2. (c) 2006 Elsevier Inc. All rights reserved.