Integral inequalities in domains of hyperbolic type and their applications. (December 2015)

• Record Type: Journal Article
• Authors: Avkhadiev, F. G.
• Is Part Of: Sbornik. Volume 206:Number 12(2015)
• Page Start: 1657
• Page End: 1681
• Publication Date: 2015-12
• Subjects: Primary 30C20; Poincaré metric -- conformal mappings -- uniformly perfect sets -- Hardy's inequalities.; Mathematics -- Periodicals; 510.5
• DOI: 10.1070/SM2015v206n12ABEH004508
• Languages: English
• ISSNs: 1064-5616

Abstract

Abstract: 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.