Banach Journal of Mathematical Analysis

Three-parameter weighted Hardy type inequalities

R. Oinarov and A. Kalybay

Full-text: Open access

Abstract

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.

Article information

Source
Banach J. Math. Anal., Volume 2, Number 2 (2008), 85-93.

Dates
First available in Project Euclid: 21 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1240336295

Digital Object Identifier
doi:10.15352/bjma/1240336295

Mathematical Reviews number (MathSciNet)
MR2436869

Zentralblatt MATH identifier
1173.26317

Subjects
Primary: 26D10: Inequalities involving derivatives and differential and integral operators
Secondary: 26D15: Inequalities for sums, series and integrals 46E15: Banach spaces of continuous, differentiable or analytic functions 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Keywords
inequalities Hardy type inequalities weight functions

Citation

Oinarov, R.; Kalybay, A. Three-parameter weighted Hardy type inequalities. Banach J. Math. Anal. 2 (2008), no. 2, 85--93. doi:10.15352/bjma/1240336295. https://projecteuclid.org/euclid.bjma/1240336295


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