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Matematicheskie Zametki, 2017, Volume 101, Issue 4, Pages 483–502
DOI: https://doi.org/10.4213/mzm11155 (Mi mzm11155) 		 
This article is cited in 4 scientific papers (total in 4 papers)

The Logarithm of the Modulus of a Holomorphic Function as a Minorant for a Subharmonic Function. II. The Complex Plane

T. Yu. Baiguskarov, B. N. Khabibullin, A. V. Khasanova

Bashkir State University, Ufa
Full-text PDF (678 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm11155
Abstract: Let $u\not\equiv-\infty$ be a subharmonic function in the complex plane. We establish necessary and/or sufficient conditions for the existence of a nonzero entire function $f$ for which the modulus of the product of each of its $k$th derivative $k=0,1,\dots$, by any polynomial $p$ is not greater than the function $Ce^u$ in the entire complex plane, where $C$ is a constant depending on $k$ and $p$. The results obtained significantly strengthen and develop a number of results of Lars Hörmander (1997).
Keywords: entire function, subharmonic function, integral mean, Riesz measure, counting function.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00024
This work was supported by the Russian Foundation for Basic Research under grant 16-01-00024.
Received: 11.03.2016
Revised: 14.06.2016
English version:
Mathematical Notes, 2017, Volume 101, Issue 4, Pages 590–607
DOI: https://doi.org/10.1134/S000143461703018X
Bibliographic databases:
Document Type: Article
UDC: 517.53+517.574
Language: Russian
Citation: T. Yu. Baiguskarov, B. N. Khabibullin, A. V. Khasanova, “The Logarithm of the Modulus of a Holomorphic Function as a Minorant for a Subharmonic Function. II. The Complex Plane”, Mat. Zametki, 101:4 (2017), 483–502; Math. Notes, 101:4 (2017), 590–607
Citation in format AMSBIB
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\paper The Logarithm of the Modulus of a Holomorphic Function as a Minorant for a Subharmonic Function. II.~The Complex Plane
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\pages 483--502
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