Geodesic
Sharp Hardy type inequalities with weights depending on Bessel function
Ufa mathematical journal, Tome 9 (2017) no. 1, pp. 89-97

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We prove exact Hardy type inequalities with the weights depending on a Bessel function. We obtain one-dimensional $L^p$-inequalities and provide an example of extending these inequalities for the case of convex domains with a finite inner radius. The proved statements are generalization for the case of arbitrary $p\geqslant2$ of the corresponding inequality proved by F. G. Avkhadiev and K.-J. Wirths for $p=2$.
Keywords: Hardy inequality, Bessel function, distance function, inner radius
Mots-clés : Lamb constant, convex domains. 
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     author = {R. G. Nasibullin},
     title = {Sharp {Hardy} type inequalities with weights depending on {Bessel} function},
     journal = {Ufa mathematical journal},
     pages = {89--97},
     publisher = {mathdoc},
     volume = {9},
     number = {1},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UFA_2017_9_1_a7/}
}
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R. G. Nasibullin. Sharp Hardy type inequalities with weights depending on Bessel function. Ufa mathematical journal, Tome 9 (2017) no. 1, pp. 89-97. http://geodesic.mathdoc.fr/item/UFA_2017_9_1_a7/