On strong tracts of subharmonic functions of finite lower order

I. I. Marchenko; A. Szkibiel

We define the notion of a strong asymptotic tract for subharmonic function of finite lower order $\lambda$. We estimate the number of strong tracts using Petrenko's magnitude of the deviation from $\infty$ of a subharmonic function $u(z)$. The estimates in the paper are exact.

1. Hayman W.K., Kennedy P.B. Subharmonic functions. Vol. I, Academic Press, 1976.

2. Talpur M.N.M. A subharmonic analogue of Iversen's theorem., Proc. London Math. Soc.(3) 32 (1976), 181–192.

3. Hayman W.K. Subharmonic functions. Vol. II, Academic Press, 1989.

4. Петренко В.П. Рост мероморфных функций конечного нижнего порядка, Изв. Акад. наук СССР, 33 (1969), № 2, 414–454.

5. Марченко И.И. Об асимптотических значениях целых функций, Изв. РАН, сер. матем. 63 (1999), № 3, 133–146.

6. Baernstein A. Integral means, univalent functions and circular symmetrization, Acta Math. 133 (1974), no. 3–4, 139–169.

7. Hayman W.K. Multivalent Functions, Cambridge Univ. Press, Cambridge 1958.

8. Gariepy R., Lewis J.L. Space Analogues of some theorems for subharmonic and meromorphic functions, Ark. Mat. 13 (1975), 91–105.

9. Marchenko I.I. On the magnitudes of deviations and spreads of meromorphic functions of finite lower order, Mat.Sb. 186 (1995), 391–408.

10. Essen M. and Shea D.F. Applications of Denjoy integral inequalities and differential inequalities to growth problems for subharmonic and meromorphic functions, Proc. Roy. Irish Acad. A82 (1982), 201–216.

11. Петренко В.П. Рост мероморфных функций.– Харьков: Вища шк., 1978.– 136 с.

	On strong tracts of subharmonic functions of finite lower order
Author	I. I. Marchenko, A. Szkibiel. marchenko@wmf.univ.szczecin.pl, olaszkibiel@poczta.onet.pl Kharkiv State University ,Institute of Mathematics, University of Szczecin
Abstract	We define the notion of a strong asymptotic tract for subharmonic function of finite lower order $\lambda$. We estimate the number of strong tracts using Petrenko's magnitude of the deviation from $\infty$ of a subharmonic function $u(z)$. The estimates in the paper are exact.
Keywords	strong asymptotic tract, subharmonic function, finite lower order
DOI	doi:10.30970/ms.22.1.35-44
Reference	1. Hayman W.K., Kennedy P.B. Subharmonic functions. Vol. I, Academic Press, 1976. 2. Talpur M.N.M. A subharmonic analogue of Iversen's theorem., Proc. London Math. Soc.(3) 32 (1976), 181–192. 3. Hayman W.K. Subharmonic functions. Vol. II, Academic Press, 1989. 4. Петренко В.П. Рост мероморфных функций конечного нижнего порядка, Изв. Акад. наук СССР, 33 (1969), № 2, 414–454. 5. Марченко И.И. Об асимптотических значениях целых функций, Изв. РАН, сер. матем. 63 (1999), № 3, 133–146. 6. Baernstein A. Integral means, univalent functions and circular symmetrization, Acta Math. 133 (1974), no. 3–4, 139–169. 7. Hayman W.K. Multivalent Functions, Cambridge Univ. Press, Cambridge 1958. 8. Gariepy R., Lewis J.L. Space Analogues of some theorems for subharmonic and meromorphic functions, Ark. Mat. 13 (1975), 91–105. 9. Marchenko I.I. On the magnitudes of deviations and spreads of meromorphic functions of finite lower order, Mat.Sb. 186 (1995), 391–408. 10. Essen M. and Shea D.F. Applications of Denjoy integral inequalities and differential inequalities to growth problems for subharmonic and meromorphic functions, Proc. Roy. Irish Acad. A82 (1982), 201–216. 11. Петренко В.П. Рост мероморфных функций.– Харьков: Вища шк., 1978.– 136 с.
Pages	35-44
Volume	22
Issue	1
Year	2004
Journal	Matematychni Studii
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