Open Access
2008 Three-parameter weighted Hardy type inequalities
R. Oinarov, A. Kalybay
Banach J. Math. Anal. 2(2): 85-93 (2008). DOI: 10.15352/bjma/1240336295


For positive integer r and real numbers $1\leq p\leq q$ we find necessary and sufficient conditions for the validity of the following inequality: \begin{eqnarray*}\left(\int\limits_a^bu(x)\left(\int\limits_a^x|g(x)-g(t)|^rw(t)dt \right)^{\frac{q}{r}}dx\right)^{\frac{1}{q}}\leq C\left( \int\limits_a^bv(x)|g'(x)|^pdx\right)^{\frac{1}{p}},\end{eqnarray*} where $u(\cdot)$, $v(\cdot)$, and $w(\cdot)$ are weight functions.


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R. Oinarov. A. Kalybay. "Three-parameter weighted Hardy type inequalities." Banach J. Math. Anal. 2 (2) 85 - 93, 2008.


Published: 2008
First available in Project Euclid: 21 April 2009

zbMATH: 1173.26317
MathSciNet: MR2436869
Digital Object Identifier: 10.15352/bjma/1240336295

Primary: 26D10
Secondary: 26D15 , ‎46E15 , 46E30

Keywords: Hardy type inequalities , Inequalities‎ , weight functions

Rights: Copyright © 2008 Tusi Mathematical Research Group

Vol.2 • No. 2 • 2008
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