Abstract. In two previous papers we generalized four classical inequalities of Hardy and Littlewood. Now it is proved that the converses of our inequalities hold if and only if the sequence of multipliers appearing in the inequalities behaves very similar to a geometrical sequence.

AMS Subject Classification (1991): 40A05

Keyword(s): inequalities

Received February 5, 1992. (Registered under 5542/2009.)