ON REGULARITY THEOREMS FOR LINEARLY INVARIANT FAMILIES OF HARMONIC FUNCTIONS
The classical theorem of growth regularity in the class S of analytic and univalent in the unit disc ∆ functions ƒ describes the growth character of different functionals of ƒ Є S and z Є ∆ as z tends to δ∆. Earlier the authors proved the theorems of growth and decrease regularity for harmonic and s...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Petrozavodsk State University
2015-05-01
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| Series: | Проблемы анализа |
| Subjects: | |
| Online Access: | http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=2910&lang=en |
| Summary: | The classical theorem of growth regularity in the class S of analytic and univalent in the unit disc ∆ functions ƒ describes the growth character of different functionals of ƒ Є S and z Є ∆ as z tends to δ∆. Earlier the authors proved the theorems of growth and decrease regularity for harmonic and sense-preserving in ∆ 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. |
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| ISSN: | 2306-3424 2306-3432 |