Geodesic
The geometry of one-dimensional and spatial Hardy type inequalities
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2022), pp. 52-88

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The proofs of many hardy-type inequalities are based on one-dimensional inequalities. The difficulties that come from the domains of integration are implicitly reflected in the one-dimensional inequalities on the interval used to substantiate the spatial analogs. One-dimensional inequalities are the analytical basis for solving geometric problems. The paper provides a brief overview of the results in this direction. An attempt is made to systematically present the theory of Hardy-type inequalities with additional terms involving the geometric characteristics of the regions, for example, such as the volume, diameter, inner radius, or the maximum conformal modulus of the region.
Keywords: Hardy's inequality, additional term, diameter, inner radius, one-dimensional inequality, spatial inequality, Bessel function, Poincaré metric.
Mots-clés : volume, maximal conformal modulus, convex domain 
@article{IVM_2022_11_a4,
     author = {R. G. Nasibullin},
     title = {The geometry of one-dimensional and spatial {Hardy} type inequalities},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {52--88},
     publisher = {mathdoc},
     number = {11},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2022_11_a4/}
}
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R. G. Nasibullin. The geometry of one-dimensional and spatial Hardy type inequalities. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2022), pp. 52-88. http://geodesic.mathdoc.fr/item/IVM_2022_11_a4/