Weighted Hardy and Opial-type inequalities (Q1192540)

A characterization of weights \(u,v\) is given for which the Hardy operator \(Hf(x)=\int^ x_ af(t)dt\) is bounded from \(L^ p((a,b);u dx)\) into \(L^ q((a,b);v dx)\) with \(0<q<1<p<\infty\) (Section 2). In Section 3 the author shows that Opial-type inequalities easily follow from inequalities of Hardy type.