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Sbornik: Mathematics, 2015, Volume 206, Issue 12, Pages 1657–1681
DOI: https://doi.org/10.1070/SM2015v206n12ABEH004508 (Mi sm8477) 		 
This article is cited in 32 scientific papers (total in 33 papers)

Integral inequalities in domains of hyperbolic type and their applications

F. G. Avkhadiev

Kazan (Volga Region) Federal University
English version PDF (591 kB) Citations (33) Russian version article
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DOI: https://doi.org/10.1070/SM2015v206n12ABEH004508
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.
Keywords: Poincaré metric, conformal mappings, uniformly perfect sets, Hardy's inequalities.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00351
15-41-02433-поволжье
This research was supported by the Russian Foundation for Basic Research (grant nos. 14-01-00351 and 15-41-02433).
Received: 17.01.2015 and 21.07.2015
Bibliographic databases:
Document Type: Article
UDC: 517.54
MSC: 30C20
Language: English
Original paper language: Russian
Citation: F. G. Avkhadiev, “Integral inequalities in domains of hyperbolic type and their applications”, Sb. Math., 206:12 (2015), 1657–1681
Citation in format AMSBIB
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\vol 206
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  • https://doi.org/10.1070/SM2015v206n12ABEH004508
  • https://www.mathnet.ru/eng/sm/v206/i12/p3
    • This publication is cited in the following 33 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник Sbornik: Mathematics
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    Abstract page:837
    Russian version PDF:202
    English version PDF:38
    References:123
    First page:230
     
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