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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
On regularity theorems for linearly invariant families of harmonic functions
E. G. Ganenkova, V. V. Starkov Petrozavodsk State University,
33, Lenina st., 185910 Petrozavodsk, Russia
Аннотация:
The classical theorem of growth regularity in the class $S$ of analytic and univalent in the unit disc $\Delta$
functions $f$ describes the growth character of different functionals of $f\in S$ and $z\in \Delta$
as $z$ tends to $\partial\Delta.$ Earlier the authors proved the theorems of growth and decrease regularity for harmonic and sense-preserving in $\Delta$ functions which generalized the classical result for the class $S.$ In the presented paper we establish new properties of harmonic sense-preserving functions, connected with the regularity theorems. The effects both common for analytic and harmonic case and specific for harmonic functions are displayed.
Ключевые слова:
regularity theorem, linearly invariant family, harmonic function.
Поступила в редакцию: 14.05.2015 Исправленный вариант: 03.09.2015
Образец цитирования:
E. G. Ganenkova, V. V. Starkov, “On regularity theorems for linearly invariant families of harmonic functions”, Пробл. анал. Issues Anal., 4(22):1 (2015), 38–56
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/pa187 https://www.mathnet.ru/rus/pa/v22/i1/p38
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