Hardy’s inequality and hausdorff operators on rearrangement-invariant morrey spaces

We generalize the Minkowski inequality, the Hardy–Littlewood–P´olya inequalities and the Hardy inequalities to rearrangement-invariant Morrey spaces. We obtain these results by extending the notion of Boyd’s indices to the rearrangement-invariant Morrey spaces. Our method also applied to establish the boundedness of Hausdorff operators on rearrangement-invariant Morrey spaces. Copyright © 2016 University of Debrecen.