Some estimates for Bochner–Riesz operators on the weighted Herz-type Hardy spaces

Abstract

In this paper, by using the atomic decomposition and molecular characterization of the homogeneous and non-homogeneous weighted Herz-type Hardy spaces H K ˙ q α , p ( w 1 , w 2 ) ( H K q α , p ( w 1 , w 2 ) ) , we obtain some weighted boundedness properties of the Bochner–Riesz operator and the maximal Bochner–Riesz operator on these spaces for α = n ( 1 / p − 1 / q ) , 0 < p ⩽ 1 and 1 < q < ∞ .