Geodesic
Holomorphic Minorants of Plurisubharmonic Functions
Funkcionalʹnyj analiz i ego priloženiâ, Tome 50 (2016) no. 1, pp. 76-79

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Let $\varphi$ be a plurisubharmonic function on a pseudoconvex domain $D$ in an $n$-dimensional complex space. We show that there exists a nonzero holomorphic function $f$ on $D$ such that some local mean value of $\varphi$ with logarithmic additional terms majorizes $\log |f|$. A similar problem is discussed for a locally integrable function on $D$ in terms of balayage of positive measures.
Keywords: holomorphic function, plurisubharmonicity, Jensen inequality, mean value in the ball.
Mots-clés : minorant, balayage 
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     author = {T. Yu. Baiguskarov and B. N. Khabibullin},
     title = {Holomorphic {Minorants} of {Plurisubharmonic} {Functions}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     publisher = {mathdoc},
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     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2016_50_1_a6/}
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T. Yu. Baiguskarov; B. N. Khabibullin. Holomorphic Minorants of Plurisubharmonic Functions. Funkcionalʹnyj analiz i ego priloženiâ, Tome 50 (2016) no. 1, pp. 76-79. http://geodesic.mathdoc.fr/item/FAA_2016_50_1_a6/