Holomorphic minorants of plurisubharmonic functions

Abstract

Let $\phi$ be a plurisubharmonic function on a pseudoconvex domain $D\subset {\mathbb{C}}^n$. We show that there exists a nonzero holomorphic function $f$ on $D$ such that some local mean value of $\phi$ 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. Key words: holomorphic function, plurisubharmonicity, minorant, balayage, Jensen inequality, mean value in the ball.

4 pages, in Russian

Cited by in corpus (1)

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