Geodesic
Hardy-Type Inequalities on Planar and Spatial Open Sets
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximation theory, and nonlinear analysis, Tome 255 (2006), pp. 8-18

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Several Hardy-type inequalities with explicit constants are proved for compactly supported smooth functions on open sets in the Euclidean space $\mathbb R^n$. 
@article{TM_2006_255_a1,
     author = {F. G. Avkhadiev},
     title = {Hardy-Type {Inequalities} on {Planar} and {Spatial} {Open} {Sets}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {8--18},
     publisher = {mathdoc},
     volume = {255},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2006_255_a1/}
}
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F. G. Avkhadiev. Hardy-Type Inequalities on Planar and Spatial Open Sets. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximation theory, and nonlinear analysis, Tome 255 (2006), pp. 8-18. http://geodesic.mathdoc.fr/item/TM_2006_255_a1/