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Probl. Anal. Issues Anal., 2015, Volume 4(22), Issue 1, Pages 38–56 (Mi pa187)  

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

Abstract: 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.

Keywords: regularity theorem, linearly invariant family, harmonic function

DOI: https://doi.org/10.15393/j3.art.2015.2910

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Bibliographic databases:

Document Type: Article
UDC: 517.57
MSC: 30C55
Received: 14.05.2015
Revised: 03.09.2015
Language: English

Citation: E. G. Ganenkova, V. V. Starkov, “On regularity theorems for linearly invariant families of harmonic functions”, Probl. Anal. Issues Anal., 4(22):1 (2015), 38–56

Citation in format AMSBIB
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\by E.~G.~Ganenkova, V.~V.~Starkov
\paper On regularity theorems for linearly invariant families of harmonic functions
\jour Probl. Anal. Issues Anal.
\yr 2015
\vol 4(22)
\issue 1
\pages 38--56
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\crossref{https://doi.org/10.15393/j3.art.2015.2910}
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