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Higher order Hardy inequalities. (English) Zbl 0802.26006
This note deals with the inequality \[ \left( \int^ b_ a \bigl | u(x) \bigr |^ q w_ 0 (x)dx \right)^{1/q} \leq C \left( \int^ b_ a \bigl | u^{(k)} (x) \bigr |^ pw_ k (x)dx \right)^{1/p}, \tag{1} \] more precisely, with conditions on the parameter \(p>1\), \(q>0\) and on the weight functions \(w_ 0\), \(w_ k\) (measurable and positive almost everywhere) which ensure that (1) holds for all functions \(u\) from a certain class \(K\) with a constant \(C>0\) independent of \(u\).
Reviewer: A.Kufner (Praha)

MSC:
26D10 Inequalities involving derivatives and differential and integral operators
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