Geodesic
The Logarithm of the Modulus of a Holomorphic Function as a Minorant for a Subharmonic Function
Matematičeskie zametki, Tome 99 (2016) no. 4, pp. 588-602

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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, logarithmic potential.
Mots-clés : Poisson–Jensen formula 
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     author = {B. N. Khabibullin and T. Yu. Baiguskarov},
     title = {The {Logarithm} of the {Modulus} of a {Holomorphic} {Function} as a {Minorant} for a {Subharmonic} {Function}},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
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B. N. Khabibullin; T. Yu. Baiguskarov. The Logarithm of the Modulus of a Holomorphic Function as a Minorant for a Subharmonic Function. Matematičeskie zametki, Tome 99 (2016) no. 4, pp. 588-602. http://geodesic.mathdoc.fr/item/MZM_2016_99_4_a10/