Geodesic
A Remark on $k$th Order Hardy Inequalities
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Studies on function theory and differential equations, Tome 248 (2005), pp. 144-152.

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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. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Studies on function theory and differential equations, Tome 248 (2005), pp. 144-152. http://geodesic.mathdoc.fr/item/TM_2005_248_a14/

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