Geodesic
On weighted norm integral inequality of g. h. Hardy's type
Kragujevac Journal of Mathematics, Tome 29 (2006), p. 165

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Zbl
In this paper, we give a necessary and sufficient condition on Hardy's integral inequality: \begin{equation}\label{ort_cond} \int_{X}[Tf]^{p}wd\mu \leq C\int_{X}f^{p}vd\mu\;\;\;\;\;\forall f \geq 0 \end{equation} where $w, v$ are non-negative measurable functions on $X$, a non-negative function $f$ defined on $(0, \infty), K(x,y)$ is a non-negative and measurable on $X \times X$, $(Tf)(x)= \int^{\infty}_{0}K(x,y)f(y)dy $ and $C$ is a constant depending on $K, p$ but independent of $f$. This work is a continuation of our recent result in \cite{RauGVM1}.
Classification : 26D15 42B30
Keywords: integral inequality, Hardy's integral inequality 
K. Rauf; J. O. Omolehin. On weighted norm integral inequality of g. h. Hardy's type. Kragujevac Journal of Mathematics, Tome 29 (2006), p. 165 . http://geodesic.mathdoc.fr/item/KJM_2006_29_a16/
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     author = {K. Rauf and J. O. Omolehin},
     title = {On weighted norm integral inequality of g. h. {Hardy's} type},
     journal = {Kragujevac Journal of Mathematics},
     pages = {165 },
     year = {2006},
     volume = {29},
     zbl = {1164.26351},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2006_29_a16/}
}
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