Sharp estimates for Hausdorff operators on complementary local Morrey-type spaces

Abstract

In this paper, some necessary and sufficient conditions for the boundedness of some linear and multilinear Hausdorff operators are established and the corresponding sharp constants are also given. Our main results can apply to some concrete operators, such as the Hardy operator and its adjoint operator, the weighted Hardy–Littlewood average, the multilinear Hardy operator and so on.