Abstract
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 (integral(b)(a) (integral(t)(a) f integral(t)(a) g)(q) w(t) dt)(1/q) <= C (integral(b)(a) f(v1)(p1))(1/p1) (integral(b)(a) f(v2)(p2))(1/p2) for all non-negative f, g on (a, b), for 1 < p1, p2, q < infinity.
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.