This article is cited in 4 papers

Brief communications

Holomorphic Minorants of Plurisubharmonic Functions

T. Yu. Baiguskarov, B. N. Khabibullin

Bashkir State University, Ufa

Abstract: 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, minorant, balayage, Jensen inequality, mean value in the ball.

Received: 03.04.2015

DOI: 10.4213/faa3225

 English version: Functional Analysis and Its Applications, 2016, 50:1, 62–65

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