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On some subclasses of delta-subharmonic functions with nonnegative harmonic majorants in the half-plane. (English. Russian original) Zbl 1354.31001

J. Contemp. Math. Anal., Armen. Acad. Sci. 51, No. 3, 134-147 (2016); translation from Izv. Nats. Akad. Nauk Armen., Mat. 51, No. 3, 9-27 (2016).
Summary: The paper is devoted to the construction in the half-plane, for delta-subharmonic functions, of an analog of the part of the theory of M. M. Djrbashian-V. S. Zakarian, which relates to the factorization of the \(\omega\)-weighted subclasses of meromorphic functions of bounded type in the unit disc. Some \(\omega\)-weighted classes of delta-subharmonic functions with bounded Tsuji type characteristics are introduced in the upper half-plane and the descriptive representations of these classes are found.

MSC:

31A05 Harmonic, subharmonic, superharmonic functions in two dimensions
31A20 Boundary behavior (theorems of Fatou type, etc.) of harmonic functions in two dimensions
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References:

[1] A. M. Jerbashian and J. E. Restrepo, “On some classes of harmonic functions with nonnegative harmonic majorants in the half-plane”, Journal of ContemporaryMathematical Analysis (National Academy of Sciences of Armenia), 51 2, 79-89, 2016. · Zbl 1344.31002
[2] E. D. Solomentsev, “On Classes of Functions Subharmonic in the Half-Space”, Vestnik MGU, Ser. Mat., 5, 73-91, 1959.
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