Geodesic
On weighted norm integral inequality of g. h. Hardy's type
Kragujevac Journal of Mathematics, Tome 29 (2006) no. 1.

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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}. 
@article{KJM_2006_29_1_a16,
     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 - 173},
     publisher = {mathdoc},
     volume = {29},
     number = {1},
     year = {2006},
     zbl = {1164.26351},
     url = {http://geodesic.mathdoc.fr/item/KJM_2006_29_1_a16/}
}
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K. Rauf; J. O. Omolehin. On weighted norm integral inequality of g. h. Hardy's type. Kragujevac Journal of Mathematics, Tome 29 (2006) no. 1. http://geodesic.mathdoc.fr/item/KJM_2006_29_1_a16/