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arXiv · 1603.01878

Holomorphic minorants of plurisubharmonic functions

B. N. Khabibullin·T. Yu. Baiguskarov
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Abstract

Let $φ$ 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 $φ$ 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.

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B. N. Khabibullin, T. Yu. Baiguskarov. 2016-05-12. Holomorphic minorants of plurisubharmonic functions. https://arxiv.org/abs/1603.01878

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