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 cases of equality are pointed out. By using these results and some recent results by the present authors (see [3]), we prove some new reversed inequalities of Hardy type for quasi-monotone functions. In some cases we obtain the best constants and all cases of equality are obtained. Some applications, open questions and the relations to other similar results are pointed out.