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Sbornik: Mathematics, 2017, Volume 208, Issue 8, Pages 1225–1245
DOI: https://doi.org/10.1070/SM8918 (Mi sm8918) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Conditions for subharmonicity and subharmonic extensions of functions

A. V. Pokrovskii

Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev
English version PDF (536 kB) Citations (3)
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DOI: https://doi.org/10.1070/SM8918
Abstract: It is shown that the well-known local Blaschke-Privalov condition, which distinguishes the subharmonic functions in the set of real upper semicontinuous functions in a fixed Euclidean domain $G$ in terms of integral mean values over balls, can be replaced by other, a priori weaker, local conditions of this type on certain subsets of $G$. Both classical and new results on removable singularities of harmonic and subharmonic functions are obtained as consequences of the central theorem.
Bibliography: 28 titles.
Keywords: subharmonic function, Blaschke-Privalov condition, inner Hausdorff measure, inner capacity, removable set.
Received: 25.01.2017 and 06.06.2017
Russian version:
Matematicheskii Sbornik, 2017, Volume 208, Number 8, Pages 145–167
DOI: https://doi.org/10.4213/sm8918
Bibliographic databases:
Document Type: Article
UDC: 517.574
MSC: 31A05, 31B05
Language: English
Original paper language: Russian
Citation: A. V. Pokrovskii, “Conditions for subharmonicity and subharmonic extensions of functions”, Mat. Sb., 208:8 (2017), 145–167; Sb. Math., 208:8 (2017), 1225–1245
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm/v208/i8/p145
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник Sbornik: Mathematics
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    Abstract page:391
    Russian version PDF:61
    English version PDF:21
    References:56
    First page:20
     
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