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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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/

[1] E. Bombieri, Invent. Math., 10 (1970), 248–263 | DOI | MR

[2] L. Hörmander, Notions of Convexity, Birkhäuser, Boston, 1994 | MR | Zbl

[3] P. Lelon, L. Gruman, Tselye funktsii mnogikh kompleksnykh peremennykh, Mir, M., 1989 | MR

[4] B. N. Khabibullin, Izv. RAN, cer. matem., 65:5 (2001), 167–190 | DOI | MR | Zbl

[5] B. N. Khabibullin, Izv. AN SSSR, cer. matem., 55:5 (1991), 1101–1123 | MR

[6] O. V. Epifanov, Matem. zametki, 51:1 (1992), 83–92 | MR | Zbl

[7] T. Yu. Baiguskarov, G. R. Talipova, B. N. Khabibullin, Algebra i analiz, 2016 (to appear)

[8] U. Kheiman, P. Kennedi, Subgarmonicheskie funktsii, Mir, M., 1980 | MR

[9] B. N. Khabibullin, T. Yu. Baiguskarov, Matem. zametki, 99:4 (2016), 591–605 | DOI