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Mat. Zametki, 2016, Volume 99, Issue 4, Pages 588–602 (Mi mz10953)  

This article is cited in 8 scientific papers (total in 8 papers)

The Logarithm of the Modulus of a Holomorphic Function as a Minorant for a Subharmonic Function

B. N. Khabibullin*, T. Yu. Baiguskarov

Bashkir State University, Ufa

Abstract: For an arbitrary subharmonic function not identically equal to $-\infty$ in a domain $D$ of the complex plane $\mathbb C$, we prove the existence of a nonzero holomorphic function in $D$ the logarithm of whose modulus is majorized by locally averaging a subharmonic function with logarithmic additions or even without them in the case $D=\mathbb C$.

Keywords: subharmonic function, minorant for a subharmonic function, holomorphic function, Riesz measure, Poisson–Jensen formula, logarithmic potential.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00030
This work was supported by the Russian Foundation for Basic Research under grant 13-01-00030.

* Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/mzm10953

Full text: PDF file (602 kB)
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English version:
Mathematical Notes, 2016, 99:4, 576–589

Bibliographic databases:

UDC: 517.53+517.574
Received: 16.04.2015
Revised: 15.09.2015

Citation: B. N. Khabibullin, T. Yu. Baiguskarov, “The Logarithm of the Modulus of a Holomorphic Function as a Minorant for a Subharmonic Function”, Mat. Zametki, 99:4 (2016), 588–602; Math. Notes, 99:4 (2016), 576–589

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. T. Yu. Baiguskarov, B. N. Khabibullin, “Holomorphic Minorants of Plurisubharmonic Functions”, Funct. Anal. Appl., 50:1 (2016), 62–65  mathnet  crossref  crossref  mathscinet  isi  elib
    2. B. N. Khabibullin, F. B. Khabibullin, “O mnozhestvakh needinstvennosti dlya prostranstv golomorfnykh funktsii”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2016, no. 4(35), 108–115  mathnet  crossref
    3. T. Yu. Baiguskarov, B. N. Khabibullin, A. V. Khasanova, “The Logarithm of the Modulus of a Holomorphic Function as a Minorant for a Subharmonic Function. II. The Complex Plane”, Math. Notes, 101:4 (2017), 590–607  mathnet  crossref  crossref  mathscinet  isi  elib
    4. R. A. Baladai, B. N. Khabibullin, “From the integral estimates of functions to uniform and locally averaged”, Russian Math. (Iz. VUZ), 61:10 (2017), 11–20  mathnet  crossref  isi
    5. B. N. Khabibullin, A. V. Shmelyova, “Balayage of measures and subharmonic functions on a system of rays. I. Classic case”, St. Petersburg Math. J., 31:1 (2020), 117–156  mathnet  crossref  isi  elib
    6. B. N. Khabibullin, F. B. Khabibullin, “K raspredeleniyu nulevykh mnozhestv golomorfnykh funktsii. III. Teoremy obrascheniya”, Funkts. analiz i ego pril., 53:2 (2019), 42–58  mathnet  crossref  mathscinet  elib
    7. B. N. Khabibullin, A. P. Rozit, E. B. Khabibullina, “Poryadkovye versii teoremy Khana—Banakha i ogibayuschie. II. Primeneniya v teorii funktsii”, Kompleksnyi analiz. Matematicheskaya fizika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 162, VINITI RAN, M., 2019, 93–135  mathnet  mathscinet
    8. E. B. Menshikova, B. N. Khabibullin, “A criterion for the sequence of roots of holomorphic function with restrictions on its growth”, Russian Math. (Iz. VUZ), 64:5 (2020), 49–55  mathnet  crossref  crossref  isi
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