Weighted Hardy and Opial-type inequalities. (English) Zbl 0756.26011

Sinnamon, G. J.

J. Math. Anal. Appl. 160, No. 2, 434-445 (1991).

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.

Reviewer: B.Opic (Praha)

MSC:

26D10	Inequalities involving derivatives and differential and integral operators
26D15	Inequalities for sums, series and integrals

Keywords:

Hardy-type inequality; Opial-type inequality; weighted Lebesgue spaces; Hardy operator

References:

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