Abstract. If we consider the class of (quasi-)monotone functions, then Hardy's classical inequalities hold also in the reversed direction for {\it some} constants. In this paper we present several proofs of these reversed Hardy's inequalities, which, in particular, give the best possible constants in all cases. The results obtained may be regarded as a unification and generalization of some results recently obtained in [2], [4] and [11].

AMS Subject Classification (1991): 26D15, 26D20

Received April 19, 1993. (Registered under 5584/2009.)