ON SOME SHARP REVERSED HOLDER AND HARDY TYPE INEQUALITIES

We discuss some reversed Holder inequalities yielding for functions on R(+) satisfying one or two conditions of quasi-monotonicity. All case s of equality are pointed out. By using these results and some recent results by the present authors (see [3]), we prove some new reversed i nequalities of Hardy type for quasi-monotone functions. In some cases we obtain the best constants and all cases of equality are obtained. S ome applications, open questions and the relations to other similar re sults are pointed out.