An iteration technique for characterizing boundedness of certain types of multilinear operators is presented, reducing the problem to a corresponding linear-operator case. The method gives a simple proof of a characterization of validity of the weighted bilinear Hardy inequality
for all non-negative f, g on (a, b), for 1 < p
2, q < ∞. More equivalent characterizing conditions are presented.
The same technique is applied to various further problems, in particular those involving multilinear integral operators of Hardy type.