Geodesic
Accuracy of constants in logarithmic Hardy-type inequalities in open multidimensional domains
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 3, pp. 111-125

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Multidimensional Hardy-type inequalities in arbitrary domains of the Euclidean space are investigated. Accuracy of the constants is established in the case when the inner radius of the domain is finite, and the weight function contains degrees and the multiple logarithms of the function of the distance to the domain's boundary.
Keywords: Hardy-type inequalities, logarithmic singularity, accuracy of constants, distance function. 
@article{UZKU_2013_155_3_a11,
     author = {R. G. Nasibullin},
     title = {Accuracy of constants in logarithmic {Hardy-type} inequalities in open multidimensional domains},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {111--125},
     publisher = {mathdoc},
     volume = {155},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2013_155_3_a11/}
}
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R. G. Nasibullin. Accuracy of constants in logarithmic Hardy-type inequalities in open multidimensional domains. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 3, pp. 111-125. http://geodesic.mathdoc.fr/item/UZKU_2013_155_3_a11/