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Matematicheskie Zametki, 2016, Volume 99, Issue 4, Pages 588–602
DOI: https://doi.org/10.4213/mzm10953 (Mi mzm10953) 		 
This article is cited in 13 scientific papers (total in 13 papers)

The Logarithm of the Modulus of a Holomorphic Function as a Minorant for a Subharmonic Function

B. N. Khabibullin, T. Yu. Baiguskarov

Bashkir State University, Ufa
Full-text PDF (602 kB) Citations (13)
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DOI: https://doi.org/10.4213/mzm10953
Abstract: For an arbitrary subharmonic function not identically equal to $-\infty$ in a domain $D$ of the complex plane $\mathbb C$, we prove the existence of a nonzero holomorphic function in $D$ the logarithm of whose modulus is majorized by locally averaging a subharmonic function with logarithmic additions or even without them in the case $D=\mathbb C$.
Keywords: subharmonic function, minorant for a subharmonic function, holomorphic function, Riesz measure, Poisson–Jensen formula, logarithmic potential.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-00030
This work was supported by the Russian Foundation for Basic Research under grant 13-01-00030.
Received: 16.04.2015
Revised: 15.09.2015
English version:
Mathematical Notes, 2016, Volume 99, Issue 4, Pages 576–589
DOI: https://doi.org/10.1134/S0001434616030317
Bibliographic databases:
Document Type: Article
UDC: 517.53+517.574
Language: Russian
Citation: B. N. Khabibullin, T. Yu. Baiguskarov, “The Logarithm of the Modulus of a Holomorphic Function as a Minorant for a Subharmonic Function”, Mat. Zametki, 99:4 (2016), 588–602; Math. Notes, 99:4 (2016), 576–589
Citation in format AMSBIB
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    Cycle of papers
    This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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