Geodesic
Boundedness Criterions for the Hardy Operator in Weighted Lp(.)(0,l) Space
Journal of convex analysis, Tome 22 (2015) no. 2, pp. 553-568
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Equivalent conditions are proved for the Hardy type weighted inequality $$ \Big\Vert W(\cdot)^{-1}\sigma(\cdot)^{\frac{1}{p(\cdot)}} \int_{0}^{x} f(t)dt \Big \Vert_{L^{p(\cdot)}(0,l)} \leq C \Big \Vert \omega(\cdot)^{ \frac{1}{p(\cdot)}} f \Big \Vert_{L^{p(\cdot)}(0,l)}, \; \; \; f \geq 0 $$ to be fulfilled in the norms of a Lebesgue space with variable exponent $L^{p(.)}(0,l)$. It is assumed that the function $p(.)$ is a monotone function.
Classification : 42A05, 42B25, 26D10, 35A23
Mots-clés : Hardy operator, Hardy type inequality, variable exponent, weighted inequality, necessary and sufficient condition 
@article{JCA_2015_22_2_JCA_2015_22_2_a12,
     author = {F. Mamedov and F. M. Mammadova and M. Aliyev},
     title = {Boundedness {Criterions} for the {Hardy} {Operator} in {Weighted} {L\protect\textsuperscript{p(.)}(0,l)} {Space}},
     journal = {Journal of convex analysis},
     pages = {553--568},
     year = {2015},
     volume = {22},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2015_22_2_JCA_2015_22_2_a12/}
}
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F. Mamedov; F. M. Mammadova; M. Aliyev. Boundedness Criterions for the Hardy Operator in Weighted Lp(.)(0,l) Space. Journal of convex analysis, Tome 22 (2015) no. 2, pp. 553-568. http://geodesic.mathdoc.fr/item/JCA_2015_22_2_JCA_2015_22_2_a12/