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This article is cited in 5 scientific papers (total in 5 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
Citation:
T. Yu. Baiguskarov, B. N. Khabibullin, “Holomorphic Minorants of Plurisubharmonic Functions”, Funktsional. Anal. i Prilozhen., 50:1 (2016), 76–79; Funct. Anal. Appl., 50:1 (2016), 62–65
Linking options:
https://www.mathnet.ru/eng/faa3225https://doi.org/10.4213/faa3225 https://www.mathnet.ru/eng/faa/v50/i1/p76
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Abstract page: | 391 | Full-text PDF : | 154 | References: | 95 | First page: | 60 |
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