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 Mat. Zametki, 2017, Volume 101, Issue 4, Pages 483–502 (Mi mz11155)

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

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 $k=0,1,…$, 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.

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/mzm11155

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English version:
Mathematical Notes, 2017, 101:4, 590–607

Bibliographic databases:

UDC: 517.53+517.574
Revised: 14.06.2016

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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