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Zbl 1173.26317
Oinarov, R.; Kalybay, A.
Three--parameter weighted Hardy type inequalities.
(English)
[J] Banach J. Math. Anal. 2, No. 2, 85-93, electronic only (2008). ISSN 1735-8787/e

The authors find necessary and sufficient conditions for the validity of the following inequality: $$\left( \int_{a}^{b} u(x) \left( \int_{a}^{x} |g(x)- g(t)|^{r} w(t)\,dt \right)^{\frac{q}{r}} \,dx \right)^{\frac{1}{q}} \leq C \left( \int_{a}^{b} v(x)|g'(x)|^{p}\,dx \right)^{\frac{1}{p}}$$ where \ $u(\cdot), v(\cdot), w(\cdot)$ are weight functions, $0<r< \infty$, $1\leq p \leq q < \infty$ and $C$ is the best constant.
[Dumitru Acu (Sibiu)]
MSC 2000:
*26D10 Inequalities involving derivatives, diff. and integral operators
26D15 Inequalities for sums, series and integrals of real functions

Keywords: inequalities involving and integral operators derivatives and differential; inequalities for sums, series and integrals

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