Boundedness of vector-valued operators on weighted Herz spaces

In this paper, the authors establish the weighted weak and strong type norm inequalities in the set of weighted Herz-type spaces for a vector-valued analogue of the Hardy-Littlewood maximal operator; and using this, the authors obtain the weightd inequalies for a wide class of sublinear singular operators defined onR ⁿ which include the Calderón-Zygmund operators as special cases. The fractional versions of these results are also given.