Geodesic
Integral inequalities in domains of hyperbolic type and their applications
Sbornik. Mathematics, Tome 206 (2015) no. 12, pp. 1657-1681

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New integral Hardy-type inequalities for compactly supported functions in arbitrary plane domains of hyperbolic type are given. Special cases for domains with uniformly perfect boundaries are studied and some applications are considered. The proofs depend substantially on fundamental equations and formulae for the hyperbolic metric, and use is also made of characteristics of domains in terms of moduli. These date back to Teichmüller. Bibliography: 20 titles.
Keywords: Poincaré metric, conformal mappings, uniformly perfect sets, Hardy's inequalities. 
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     author = {F. G. Avkhadiev},
     title = {Integral inequalities in domains of hyperbolic type and their applications},
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     url = {http://geodesic.mathdoc.fr/item/SM_2015_206_12_a0/}
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F. G. Avkhadiev. Integral inequalities in domains of hyperbolic type and their applications. Sbornik. Mathematics, Tome 206 (2015) no. 12, pp. 1657-1681. http://geodesic.mathdoc.fr/item/SM_2015_206_12_a0/