Geodesic
The Logarithm of the Modulus of a Holomorphic Function as a Minorant for a Subharmonic Function. II.~The Complex Plane
Matematičeskie zametki, Tome 101 (2017) no. 4, pp. 483-502

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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. 
@article{MZM_2017_101_4_a0,
     author = {T. Yu. Baiguskarov and B. N. Khabibullin and A. V. Khasanova},
     title = {The {Logarithm} of the {Modulus} of a {Holomorphic} {Function} as a {Minorant} for a {Subharmonic} {Function.} {II.~The} {Complex} {Plane}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {483--502},
     publisher = {mathdoc},
     volume = {101},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_101_4_a0/}
}
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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. Matematičeskie zametki, Tome 101 (2017) no. 4, pp. 483-502. http://geodesic.mathdoc.fr/item/MZM_2017_101_4_a0/