Geodesic
A Remark on $k$th Order Hardy Inequalities
Informatics and Automation, Studies on function theory and differential equations, Tome 248 (2005), pp. 144-152.

Voir la notice de l'article provenant de la source Math-Net.Ru

Conditions on the weight functions are derived that guarantee the validity of the higher order Hardy inequality for classes of functions satisfying rather general boundary conditions. The approach uses the Green function of a certain boundary value problem and is illustrated by the case of second-order Hardy inequality, for which even necessary and sufficient conditions are derived. 
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     author = {A. Kufner},
     title = {A {Remark} on $k$th {Order} {Hardy} {Inequalities}},
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A. Kufner. A Remark on $k$th Order Hardy Inequalities. Informatics and Automation, Studies on function theory and differential equations, Tome 248 (2005), pp. 144-152. http://geodesic.mathdoc.fr/item/TRSPY_2005_248_a14/

[1] Kufner A., Persson L.E., Weighted inequalities of Hardy type, World Sci., Singapore, 2003 | MR | Zbl