Sharp bounds for Hardy-type operators on mixed radial-angular central Morrey spaces

Abstract

Abstract By using the rotation method, a sharp bound for an n-dimensional Hardy operator on mixed radial-angular central Morrey spaces is obtained. Furthermore, a sharp weak-type estimate for an n-dimensional Hardy operator on mixed radial-angular central Morrey spaces is established. In addition, we also calculate the sharp constant for an n-dimensional m-linear Hardy operator from product mixed radial-angular central Morrey spaces to mixed radial-angular weak central Morrey spaces. Since mixed radial-angular central Morrey spaces are generalizations of both central Morrey spaces and mixed radial-angular spaces, the main theorems in this paper extend various existing results to a more general setting.

Keywords

• Hardy operator
• Sharp bound
• m-linear Hardy operator
• Mixed radial-angular central Morrey space
• Rotation method