Weighted Hardy operators in the local generalized vanishing Morrey spaces

摘要

In this paper we study p → q-boundedness of the multi-dimensional Hardy type operators in the vanishing local generalized Morrey spaces V L~(p,φ) loc(?~n, w) defined by an almost increasing function φ(r) and radial type weight w({pipe}x{pipe}). We obtain sufficient conditions, in terms of some integral inequalities imposed on φ and w, for such a boundedness. In the case where the function φ(r) and the weight are power functions, these conditions are also necessary.