The geometry of one-dimensional and spatial Hardy type inequalities

R. G. Nasibullin

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2022), pp. 52-88.

Résumé

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.

Détail

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

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