Abstract
Let φ 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 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.
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References
E. Bombieri, Invent. Math., 10 (1970), 248–263.
L. Hörmander, Notions of Convexity, Birkhäuser, Boston, 1994.
P. Lelong and L. Gruman, Entire Functions of Several Complex Variables, Springer-Verlag, Berlin, 1986.
B. N. Khabibullin, Izv. Ross. Akad. Nauk, Ser. Mat., 65:5 (2001), 167–190; English transl.: Izv. Math., 65:5 (2001), 1017–1039.
B. N. Khabibullin, Izv. Akad. Nauk SSSR, Ser. Mat., 55:5 (1991), 1101–1123; English transl.: Math. USSR Izv., 39:2 (1992), 1063–1084.
O. V. Epifanov, Mat. Zametki, 51:1 (1992), 83–92; English transl.: Math. Notes, 51:1 (1992), 54–60.
T. Yu. Baiguskarov, G. R. Talipova, and B. N. Khabibullin, Algebra i Analiz (2016), to appear.
W. K. Hayman and P. B. Kennedy, Subharmonic Functions, Academic Press, New York, 1976.
B. N. Khabibullin and T. Yu. Baiguskarov, Mat. Zametki, 99:4 (2016), 588–602; English transl.: Math. Notes, to appear.
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Supported by RFBR (project 16-01-00024a).
Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 50, No. 1, pp. 76–84, 2016
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Baiguskarov, T.Y., Khabibullin, B.N. Holomorphic Minorants of Plurisubharmonic Functions. Funct Anal Its Appl 50, 62–65 (2016). https://doi.org/10.1007/s10688-016-0129-0
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DOI: https://doi.org/10.1007/s10688-016-0129-0