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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
##### Keywords:
higher order Hardy inequalities; weight functions
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