Sharp constants for Hausdorff-type operators on power-weighted local Morrey-type spaces

Abstract

In this paper, we give necessary and sufficient conditions for the boundedness of two Hausdorff-type operators on power-weighted local Morrey-type spaces. Meanwhile, the corresponding sharp constants are also obtained. As applications, the sharp estimates of the fractional Hardy operator and its adjoint operator, the weighted Hardy–Littlewood average operator and the weighted Ces`aro operator on power-weighted local Morrey-type spaces are established.